I'm not sure Lennon would have taken Paul's death as hard as your suggesting, Lennon did not kill himself when Stuart Sutcliffe died, why would he when McCartney died? He was closer to Stu than to Paul on a personal level. This isn't to say he won't be affected, more than likely this'll bring up memories of his mother, who was run over by a speeding driver.
The thing about Lennon is, as much of a independent spirit he may have been, he had a pretty consistent need for a partner. When he was a kid it was Pete Shotton. In art school it was Stuart Sutcliffe, in the Beatles it was Paul McCartney, in his early solo career and after their reunion, it was Yoko Ono ect. With McCartney dead, John's probably going to be looking for a new partner to take his place. It probably wouldn't be Yoko Ono, though it might be a mistake to just say it'd be automatically butterflied. They might still meet, albeit under slightly different circumstances later on.
I'm not entirely sure who fits the bill for a new Lennon partner, if not Yoko, who? One might want to start by wandering around the English rock and pop scene in the time period and look for someone Lennon might want to join forces with, any ideas?
Strawberry Fields Forever was already written, and so it's probably still recorded, either as a augmented Beatles single or as a Lennon solo record, or else Lennon forms some new group, in any case it's still released. Paul's death is not going to stop him from writing music and recording anymore than Stu or Epstein's death did IOTL. So Lennon songs will still appear, though given butterflies, it's likely they are not the same songs we know from OTL with the exception of Strawberry Fields Forever, which again, was already written for the most part when Paul dies ITTL. The butterflying of Yoko might have a very adverse affect on Lennon though, while he probably has a lot of good songs in his 60's solo career, there's a good chance he's a Syd Barrett style acid casualty without Yoko.