By Charlie Savage, The New York Times WASHINGTON — Impeachment investigators are exploring whether President Donald Trump lied in his written answers to Robert Mueller during the Russia investigation, a lawyer for the House told a federal appeals court Monday, raising the prospect of bringing an additional basis for a Senate trial over whether to remove Trump. The statement — during a hearing in a case over the House’s request for secret grand-jury evidence gathered by Mueller — came shortly after Trump said he may provide written answers about the Ukraine affair to impeachment investigators. “Even though I did nothing wrong, and don’t like giving credibility to this No Due Process Hoax, I like the idea & will, in order to get Congress focused again, strongly consider it!” Trump wrote, after insulting House Speaker Nancy Pelosi. But the hearing heightened focus on House suspicions that Trump had lied to Mueller’s investigators when he provided lawyerly, written answers to some questions.