If you're talking about "Who Killed John Lennon?" written by Fenton Bresler in the 1980s, your characterization of the author and of the premise of the book are awfully simplistic and misleading. Bresler, a lawyer and and author, is hardly a left-wing nutcase. He also didn't suggest Reagan, whose rise to national political prominence is a big part of the book, had a hand in Lennon's murder. Rather, he put forth a compelling case that the politically powerful behind Reagan had the means (CIA ops) and motive (eliminating the one person the FBI perceived and documented as capable of rallying the most people against Reagan) to pull off such a hit. Do I believe the book? I don't know, but he never said Reagan had a hand in it. I don't think he'd consider Reagan aware enough to have known if any of it had ever been contemplated.
I've heard this book dismissed and ridiculed, but always by people who never read it cover to cover and checked its impressive list of footnotes and sourcing.