We must also remember that by his death, Lennon still had an unresolved beef with Harrison over Lennon backing out of George's Concert For Bangladesh in 1971.
Accounts diverge on what happened from George demanding Yoko doesn't appear on stage with John (which he found unacceptable) to John's ego not exactly secure at that point (if ever perhaps) to play second fiddle to his "little brother." They tried to bury the hatchet in 1974 with Lennon agreeing to "make up" by appearing at a Harrison concert during his Dark Horse tour at MSG. Except Lennon no showed again.
And from all accounts, afterwards neither met each other or perhaps even spoke to each other again for the rest of Lennon's life. Or to put it another way, George helped John on "Instant Karma!" and the Imagine album. But no more collaborations after the first Concert snub.
So in a haunting reality speculation, what if Lennon survived December 1980? Some thoughts:
(1) As planned, he would have conducted his first solo tour in 1981 to support Double Fantasy while also performing (with his own re-arrangements) Beatle tunes like "She Loves You," "I Want to Hold Your Hand," "Help!," etc. This fact was recently confirmed by Ken Sharp in his new book about the Double Fantasy studio sessions.
The album wouldn't have done as well because he lived (and let's admit something: Its sorta rubbish) but still probably decently received, a gold record. The tour is a big success though, even if there is a debate between fans about Lennon's re-interpretation of some of his Fab Four classics. But hey they get to see him live and playing that era of his life which he famously derided/dismissed years earlier.
(2) Speaking of which, in 1980s he would have scratched an old itch. He re-records/re-released "Help!" as the slower-ballad as he had initially envisioned and partners up in vocals with Sting, another lead-singer who's about to (or already has) quit his own then super-popular rock band at their supposed height of popularity. Even if it doesn't age well, its a big chart hit (hell lets say it goes #1) just from the combined star power alone, bridging two generations of rockers/fans (think MJ/Macca) and the memorable video is widely played on MTV.
(3) Beatles do get back together, albeit as a one-time concert appearance (Live Aid?) and/or releasing their long-in-development documentary and album(s) in the late 1980s, backed by a newly recorded "reteam" song or two which coulda been "Free As a Bird," "Real Love," "Grow Old With Me," (all Lennon demos), or Harrison's own "When We Was Fab."
Either way, the Fab Four use this opportunity to give their shared legacy/past the proper, positive public funeral instead of the bitter lawsuit-flying Let It Be divorce. Think Pink Floyd at Live 8.
(4) There might be a big hoopla over Lennon/McCartney working together again, maybe on a song here and there on each other's albums. Less World's Finest coming back to stands and more like special appearances. I'm sorry, that reference was too geeky. Apologies.
If of course each egomaniac could put aside their pride and outright ask the other to look over whatever crap they were working on separately at the time. Macca has been complimentary of numerous Lennon solo works, and Lennon notably liked Macca's "3 Legs" and especially "Coming Up."
(5) No Beatles Tour, though consider a possible outcome for comparison in The Police reunion tour. No new album or material, but guys at the bitter end were probably trying to murder each other at the studio, put aside their beefs and perform a super successful, super received "Greatest Hits" tour. Maybe in 1992 to commemorate the 30th anniversary of their first single's ("Love Me Do") release?
(6) Lennon continues for better or worse, public approval or not, speak his mind rather freely. In 1980 he had hallowed out from his late 60s/early 70s protest/activist stage, but surely something would have come along and burn his biscuits again. Maybe anti-Nukes or the Iraq War, he would have been inspired one way or another to use politics of the time to make music of the time. As we saw this can for good ("Give Peace a Chance") or bad (the tedious, self-important Sometime in New York record)