Mr. Solomon did not immediately respond to a request for comment.
The lobbying disclosure law contains an exemption for legal work, and Mr. Giuliani said his efforts to unearth information and push both for investigations in Ukraine and for news coverage of his findings originated with his defense of Mr. Trump in the special counsel’s investigation.
He acknowledged that his work morphed into a more general dragnet for dirt on Mr. Trump’s targets but said that it was difficult to separate those lines of inquiry from his original mission of discrediting the origins of the special counsel’s investigation.
Mr. Giuliani said Mr. Lutsenko never specifically asked him to try to force Ms. Yovanovitch’s recall, saying he concluded himself that Mr. Lutsenko probably wanted her fired because he had complained that she was stifling his investigations.
“He didn’t say to me, ‘I came here to get Yovanovitch fired.’ He came here because he said he had been trying to transmit this information to your government for the past year, and had been unable to do it,” Mr. Giuliani said of his meeting in New York with Mr. Lutsenko. “I transmitted the information to the right people.”
The president sought to distance himself earlier on Friday from Mr. Giuliani, saying he was uncertain when asked whether Mr. Giuliani still represented him. “I haven’t spoken to Rudy,” Mr. Trump told reporters. “I spoke to him yesterday quickly. He is a very good attorney and he has been my attorney.”
Mr. Giuliani later said that he still represented Mr. Trump.
The recall of the ambassador and the efforts by Mr. Trump and Mr. Giuliani to push for investigations in Ukraine have emerged as the focus of House Democrats’ impeachment inquiry into Mr. Trump.
The impeachment was prompted by a whistle-blower complaint about Mr. Trump pressing President Volodymyr Zelensky of Ukraine in a July phone call to pursue investigations that could help Mr. Trump’s 2020 re-election campaign. At the time, the Trump administration had frozen $391 million in military assistance to Ukraine for its fight against Russian-backed separatists.