LENNON by Ray Coleman (McGraw-Hill: $19.95). Considering John Lennon's social and musical impact, it's surprising that it has taken more than four years for someone to come up with anything resembling the definitive biography of the late rock star. Several books have given us pieces of the Lennon story, from Jon Wiener's tunnel-visioned essay on Lennon the activist ("Come Together") to such hollow "insider" accounts as Peter Brown and Steven Gaines' "The Love You Make." In this hefty (640-page) volume, Coleman, a veteran British pop journalist and editor, sets out to tell the complete story. In doing so, he has been aided greatly by the cooperation of the two people who knew Lennon best in the Liverpool days (Mary Smith, the aunt who reared him, and Cynthia Powell, his first wife) and by Lennon's closest male friend in the years after the Beatles broke up (Elliot Mintz, a former Los Angeles radio talk-show host). While Coleman doesn't betray their trust (this isn't the kind of sensation-minded book that is likely to be serialized by National Enquirer), he doesn't use the information to weave anything close to a dramatic or revealing portrait. Coleman has simply used a lot of space to tell a very familiar story, which is one of the dangers in writing about media stars. There is so much written about them during their life that it's hard to come up with noteworthy new material. That's especially true of Lennon, a wonderfully candid and articulate interview subject. The challenge in writing about Lennon (surely one of the half-dozen most influential pop figures of the rock era) is to explore the reasons for his ability to capture the imagination of a generation. That's an area that Coleman skirts. This book is far more well-intended and thorough than most rock bios, but it lacks the compelling vision or purpose that would bring it to life. After reading the book, you don't feel any closer to knowing the private Lennon, though you certainly know a lot of the things that happened to Lennon.