Nearly two dozen soldiers from an Army platoon were on patrol in a dangerous valley in southern Afghanistan when a motorcycle sped toward them, ignoring commands to stop.

As he tells it, First Lt. Clint Lorance, the platoon leader, ordered his men to fire just seconds before the motorcycle bore down on them that July day in 2012. But the Afghans were unarmed, and two died. The next year, Lieutenant Lorance was found guilty at a court-martial of second-degree murder, one of the few times an American soldier has been convicted of a crime for actions in combat in Iraq or Afghanistan. He is serving a 19-year sentence at Fort Leavenworth, Kan.

But the case is far from over. Mr. Lorance, who was dismissed from the Army, has become a cause célèbre for conservative commentators, including Sean Hannity of Fox News, who say the Obama administration punished a soldier for trying to defend his troops. Three Republican House members — Duncan Hunter of California, Matt Salmon of Arizona and Ryan Zinke of Montana — have asked the secretary of the Army to review the case. And more than 124,000 people have signed a petition to the White House demanding a pardon.

“The warfighter doesn’t always have the benefit of time, given lives are always at risk in a war zone,” the lawmakers wrote in their letter, sent in January, saying the case “deserves a high level of attention and scrutiny.”