I feel like Giuliani got himself stuck between a rock and a hard place here by filing actual lawsuits.
At that point, he either had to (1) include his claims about Dominion (which were extremely relevant to his lawsuits) and open himself up to perjury or (2) leave his claims out, providing pretty damning evidence in a defamation suit that he didn't believe the evidence himself.
He went with (2) and he only has a tiny bit of wiggle room to prove that he believed the claims / "evidence" but they wouldn't be useful to include in his lawsuits.
Powell and Wood relied on donations for their work and Wood in particular is a multi-millionaire many times over for some of the corporate work he's done. I'm sure Rudy is rich, mostly from the speech circuit post 9/11, but he's not Lin Wood rich. He probably needs to work to maintain his lifestyle.
Giuliani deserves whatever is coming to him.
This seems to be a standard trope but I've never met anyone who fit it.
It also makes you wonder why he needs to bother.
A skilled liar would never for a moment reveal that they did not truly believe what they were saying, not even in private correspondence. Even in typical, not overtly evil companies, the saying "write for the subpoena" is passed around as advice for would-be upfront communicators.
Still, if criminals never made mistakes the justice system would convict almost nobody of anything.