WASHINGTON — The White House on Monday blocked two more former aides to President Trump from testifying in House Democrats’ impeachment inquiry, but cleared a third witness, Corey Lewandowski, to appear publicly on Tuesday and answer limited questions about potential obstruction of justice by the president.

The White House decisions amounted to mixed news for the House Judiciary Committee as it tries to crank up the intensity of an investigation devised to determine whether to recommend Mr. Trump’s impeachment for obstruction of justice and abuse of power — and to convince the public that such action is warranted.

In Mr. Lewandowski, who managed Mr. Trump’s presidential campaign and remained a confidant once he became president, the judiciary panel will be getting a figure who could help bring to life evidence uncovered by Robert S. Mueller III, the special counsel who investigated Russia’s interference in the 2016 election. Though the panel has publicly quizzed legal experts and Mr. Mueller on his findings, Mr. Lewandowski will be the first fact witness referenced in Mr. Mueller’s report whom the White House has not blocked from publicly testifying entirely.

He played an important role in an attempt by the president in summer 2017 to effectively end scrutiny of Mr. Trump’s campaign, one of several episodes that Democrats have said were clear cases of obstruction. But Mr. Lewandowski is also pugnacious, fiercely loyal to Mr. Trump and contemplating a Senate run in New Hampshire — and he has pledged to “fight back” against the Democrats.