A central contention of Democratic lawmakers in that trial, in the fall of 2019, was that Mr. Trump had falsely asserted a desire to fight corruption in Ukraine by withholding military aid. In fact, they said, he withheld the aid to pressure Mr. Zelensky to investigate Mr. Biden, at the time a likely opponent in the 2020 presidential election. Mr. Trump’s personal lawyer, Rudolph W. Giuliani, had worked with associates of Mr. Kolomoisky in his efforts to uncover dirt on Mr. Biden in Ukraine.