The Beatles broke up a full ten years before John Lennon was shot. That only cemented their fame, it didn't do much to create it nor did it do anything for the band while they were active.
Plenty of bands from then have toured with original members of a couple replacements years after they initially broke up. The Rolling Stones, for instance have changed much of their line-up. Pink Floyd is another example.
If John Lennon had not been killed, the Beatles could have toured in the 80s, 90s, 2000s, 2010’s by reuniting or replacing a different member or two. Many other bands of that era have broken up and then reunited to tour.