Ah, I'm a huge Lennon fan, so I have some suggestions for you.
You can go with the party line, basically Yoko approved stuff like The Ballad of John and Yoko or Lennon by Ray Coleman.
Or you can branch out and read some rather interesting stuff like:
Dakota Days by John Green
Loving John by May Pang
John Lennon, My Brother by Julia Baird
John Lennon In My Life by Pete Shotton
A Twist of Lennon by Cynthia Lennon
The Last Days of John Lennon by Frederic Seaman
I'd say read them all. I prefer the last six books, they are more honest, I feel.