There have been TL's on this before, but none I believe on this site...
Lennon's love for art was dwarfed by his love for rock 'n' roll so any TL in which Lennon chooses art as his career path involves an early break-up of the Beatles followed by another failed project or string of them.
In this scenario, I can see Lennon following in Sutcliffe's footsteps and shifting his art from more humorous cartoons to serious Abstract Expressionism, with maybe a dark wit remaining.
As for the Beatles, they may end up doing a little better initially without Lennon. The conflict with George Martin when they first entered the studio was which one to market as the leader, John or Paul. With that problem eliminated, the music suffers with the Lennon vacuum, but Paul McCartney is a pop star and the rest of the Beatles are merely a backing band, perhaps even prompting a name change like, Paul McCartney and the Beatles or something like that. Expect more symphonic experiments with McCartney and George Martin at the helm. The Beatles go from pop rockers to an experimental orchestral ballad-oriented band... very British.
With the success of Macca's Beatles, Lennon gains fame as the great artist who was kicked out of the Beatles (or quit, or whatever) and he'll probably use that fame to return to music by the end of the sixties.
I still see him going to London and later New York and getting involved in various causes, but without ever being a loveable mop top, he may never receive the forgiveness that credibility earned him for so long IOTL... in other words, his eccentricities limit his popularity for a while.
Part of the reason many Beatle fans let him get away with his trying-to-find-himself phase with Yoko was that he was still "Their John". Without the Beatles history, he becomes an eccentric artist turned rock musician turned activist.
If he immigrates earlier, he has a better chance of musical popularity in America as a former Liverpudlian and former Beatle during the British Invasion but, as in OTL, his art will suffer the more he pursues music.
Hope that helps.