The White House narrative about why former National Security Adviser Michael Flynn was fired has long had some curious holes — and special counsel Robert Mueller’s team is stepping up his efforts to fill them in.

NBC News’s Carol Lee and Julia Ainsley reported Monday that Mueller’s team has asked several current or former White House staffers “to go through each day that Flynn remained as national security adviser and describe in detail what they knew was happening inside the White House as it related to Flynn.”

Lee and Ainsley write that Mueller’s investigators appear to be particularly interested in the question of what the president knew about Flynn’s shifting stories and, most explosively, whether Trump directed Flynn “to lie to senior officials, including [Vice President Mike] Pence, or the FBI, and if so why.”

If evidence of the latter is found (we don’t know of any yet), it could conceivably be grounds for bringing obstruction of justice charges against the president. After all, lying to the FBI is a crime. If Trump knew Flynn was guilty of that crime when he allegedly urged then-FBI Director James Comey to go easy on Flynn — let alone if Trump outright instructed Flynn to commit that crime — prosecutors would seem to have a strong case that the president’s outreach to Comey was designed to derail a law enforcement investigation.

Lying to Pence wouldn’t necessarily have been a crime. But evidence that Trump directed Flynn to deliberately mislead the vice president would raise serious questions about why the president wanted to keep the nature of his Russia contacts secret from even his top advisers — about what he was trying to hide.

To determine whether there’s a case here, Mueller is trying to get to the bottom of several murky and unanswered questions that have long surrounded the Trump team’s accounts of Flynn’s contacts with Russian Ambassador Sergey Kislyak, and of why Flynn was eventually fired.

Here are the dates of three key events in that saga:

On December 29, 2016, the day President Barack Obama announced new sanctions on Russia, Flynn and Kislyak spoke on the phone, and Flynn told the Russian diplomat that Moscow shouldn’t retaliate in response. In mid-January 2017, Trump transition officials — specifically, Vice President-elect Pence and incoming White House spokesperson Sean Spicer — falsely told the public that Flynn and Kislyak hadn’t discussed sanctions on their call. On January 24, 2017, Flynn himself made the same false claim to the FBI.

It has long been unclear when, exactly, Trump learned the truth about each of these three things.

You can frame the questions as: When did Donald Trump learn that No. 1 happened? When did Donald Trump learn that No. 2 happened? And when did Donald Trump learn about No. 3 — which, because it involves an actual crime, may be the most important question of all?

Now that Flynn has become a cooperating witness for Mueller’s team, he might be helping to provide those answers.

1) When did Trump learn that Flynn and Kislyak had talked sanctions?

One of the most important things Mueller’s team will try to establish is when Trump first learned that Flynn had, in fact, discussed sanctions with Kislyak. (Flynn now admits he asked Russia to exercise restraint in its response to President Barack Obama’s new sanctions during a December 29 phone call.)

So why did Flynn do that? One possibility is he truly was freelancing in his calls with the Russian ambassador, and that Trump only learned what he was up to much later. Perhaps Flynn was trying to carry out what he thought his boss would want, without keeping him informed on the details of what was actually said.

Perhaps Flynn and Trump never even discussed the call’s specifics. Alternatively, perhaps Flynn lied to Trump himself about the call. (Though it may be telling that the White House has never made this claim, which likely suggests that it didn’t happen.)

The other possibility, of course, is that Trump knew all along — that Flynn told him in advance that he planned to urge Kislyak to hold off on responding to the sanctions, that Trump explicitly told Flynn to send that message to Kislyak, or that Trump was briefed on what happened shortly after the call.

This scenario would make a lot of sense. Flynn was the incoming national security adviser, after all. And Trump made quite clear at the time that he wanted Russia to hold off on any sanctions-related escalation. The day after the Flynn-Kislyak call, and after Vladimir Putin’s subsequent announcement that he wouldn’t retaliate over sanctions, Trump tweeted out praise of the Russian president:

Great move on delay (by V. Putin) - I always knew he was very smart! — Donald J. Trump (@realDonaldTrump) December 30, 2016

But if this scenario were true, it would raise some serious questions for Trump. Namely...

2) When did Trump become aware that Pence and Spicer were falsely describing the Flynn-Kislyak call?

On January 12, 2017 — eight days before Trump’s inauguration — the Washington Post’s David Ignatius broke some major news in a column. He was told by a senior US official that on the day of Obama’s Russian sanctions announcement, Flynn and Kislyak had spoken on the phone.

Ignatius didn’t offer an account of what that conversation between Flynn and Kislyak was about. He just knew they spoke on that day, and questioned whether Flynn could have been trying to undercut the sanctions.

The Trump team had to decide how to respond to this story. And the response they eventually put out in public statements by both Pence and Spicer was that the call was innocuous and that the topic of sanctions never came up.

"The call centered around the logistics of setting up a call with the president of Russia and the president-elect after he was sworn in," Spicer said on January 13. "That was it. Plain and simple." Spicer added that he expected Ignatius to update his story “to more accurately reflect the events that day.” (He’d make a similar statement from the White House podium on January 23.)

“I talked to Gen. Flynn about that conversation,” Pence said on January 15. “It was strictly coincidental that they had a conversation. They did not discuss anything having to do with the United States’ decision to expel diplomats or impose censure against Russia.”

So what happened here? Why did two Trump officials end up putting out a false story? What discussions did they have beforehand — and was Trump himself involved in those discussions?

After later reporting undercut the White House line, the Trump administration gave a simple explanation to all this: that Flynn just flat-out lied to Pence (and, presumably, Spicer). In this theory, Flynn had more or less gone rogue, lying to hide his own misconduct.

But things get murkier when we return to the question of exactly what Trump knew about all this at the time — something that has never been clear.

It’s at least possible that Trump was still clueless about the true nature of the Flynn-Kislyak call at this time, and therefore didn’t know that Pence and Spicer’s story was wrong.

However, if Trump was aware of the true nature of Flynn’s call with Kislyak at this point, he would also have been aware that Pence and Spicer were falsely describing what happened to the public. That would naturally raise questions about why he let that false story be put out anyway, and whether he was trying to mislead the American people (and if so, why).

Lee and Ainsley at NBC report that Mueller is looking into whether Trump outright “directed” Flynn to lie to Pence about what happened. There’s no evidence of that yet, but Trump has long been known for pitting his aides against each other and delegating tasks to certain advisers outside the ordinary chain of command.

And if Flynn was acting at Trump’s behest, and Trump had told him not to tell anyone about it, that raises another serious question:

3) When did Trump learn that Flynn lied to the FBI — and why did he wait so long to fire him?

Finally, and perhaps most importantly, there’s the murky question of when, exactly, Trump learned that Flynn lied to the FBI about the Kislyak call — in other words, when the president learned that his sitting national security adviser had committed a crime.

This question could prove problematic for Trump for a few reasons.

Shortly after Trump’s inauguration, on January 24, FBI agents interviewed Flynn about his contacts with Kislyak. Flynn falsely told the agents that he did not discuss sanctions with Kislyak.

Two days later, on January 26, acting Attorney General Sally Yates briefed White House counsel Don McGahn on the true nature of Flynn’s contacts with Kislyak. She later testified that she did so in part because she was concerned that Flynn could be vulnerable to Russian blackmail, and that he misled Pence.

Spicer later told the White House press corps that “immediately” after this briefing from Yates, McGahn briefed Trump and some of his top aides on the matter.

Now, it’s not clear exactly what Trump was told about Flynn in this briefing. Spicer would later claim that Trump was told there was no “legal issue” with Flynn’s conduct, and Yates did testify that she declined to tell McGahn how Flynn performed during his FBI interview. So perhaps the president really wasn’t told that Flynn outright lied to the FBI at this point.

Still, if Spicer’s timeline is accurate, Trump was told of Yates’s warning about Flynn on January 26.

This timing is particularly important because of what happened the next day, January 27. Around midday, Trump called then-FBI Director James Comey and invited him to come for dinner that evening. The dinner turned out to be just the two of them, and Comey later testified that at it, Trump asked if he wanted to remain FBI director, and asked several times for his “loyalty.”

Two and a half weeks passed without Trump taking action against Flynn — a man who at least some White House officials had reason to believe lied to the vice president.

Then a pair of Washington Post stories in mid-February — revealing first that Flynn and Kislyak did discuss sanctions during the call, and then that Yates had warned the White House that Flynn was vulnerable to Russian blackmail — appeared to force action. Trump fired Flynn on the night the second story was posted, February 13.

The next morning, on February 14, Trump asked Comey to stay behind after a briefing with several officials. Once they were alone, Comey later testified, Trump urged him to go easy on Flynn, saying, “I hope you can see your way clear to letting this go, to letting Flynn go.”

The implication, as Comey elaborated under oath, seemed obvious: that Trump wanted him to be lenient toward Flynn in the investigation of the false statements he made to the FBI.

So one important unanswered question in all this is just when, exactly, Trump learned that Flynn lied to the FBI about his contacts with Kislyak, and that he appeared to be in serious legal trouble.

It is not clear if this was made clear to Trump when he was first apparently briefed about Yates’s warning, on January 26. But for whatever reason, Trump did reach out to Comey the very next day to set up a one-on-one dinner with him and ask for his loyalty. Was that an attempt to get Comey to stop pursuing the case against Flynn?

Whether or not that’s what happened, Trump certainly seems to be aware that Flynn is in legal jeopardy the next time he reaches out to Comey — when he urges that Comey let Flynn go on February 14.

And in a recent tweet, the president appeared to admit that he learned Flynn had lied to the FBI before his firing, and that, indeed, this is one of the reasons he was fired:

I had to fire General Flynn because he lied to the Vice President and the FBI. He has pled guilty to those lies. It is a shame because his actions during the transition were lawful. There was nothing to hide! — Donald J. Trump (@realDonaldTrump) December 2, 2017

This appeared to strengthen the obstruction of justice case against Trump — because it suggests Trump knew Flynn was guilty of a crime when he reached out to Comey on Flynn’s behalf. So the White House quickly tried to walk this back, claiming that Trump’s lawyer wrote the tweet and that he didn’t get the language quite right.

Finally, another important and related question that Mueller’s team is reportedly zeroing in on is why Trump waited so long to fire Flynn after getting Yates’s warning that Flynn appeared to have lied to Pence and that he was vulnerable to Russian blackmail.

One would think that lying to the vice president-elect so he’d then go out and give a false statement in public — if that is indeed what happened — would be a fireable offense. For some reason, though, Trump didn’t appear to mind it, until the accusation spilled out into the press. The reason for that delay remains a mystery — one Mueller’s team is trying to get to the bottom of.