Longtime New York restaurateur Joey Allaham visited Manhattan’s Park East Synagogue late last year with an offer for lawyer Alan Dershowitz. Come visit Doha, the capital of Qatar, by invitation of the emir.

Mr. Dershowitz says he hadn’t met Mr. Allaham before and initially demurred before agreeing to go. The professor also didn’t know he was on a list of 250 people Mr. Allaham says he and his lobbying-business partner, Nick Muzin, identified as influential in President Trump’s orbit.

The...