Yes, it was a murder but please explain why you feel it was not also an assassination. The word assassination is generally defined as a deliberate act of killing someone, especially one who is a public figure, for financial gain, on behalf of a political agenda or for obtaining personal public recognition.
Therefore I believe it is accurate to describe the killing of John Lennon as an assassination.
It’s borderline then. Calling it an “assassination” ennobles the victim and by extension our experience of the event, which I think is over the top. By that time, Lennon was a hasbeen, pop mediocrity, much like his former partner, while, surprisingly, both George and Ringo showed some talent and staying partner, even if the results weren’t anything much to write home about.