John Lennon was a 20th century Human musician from the Earth band known as The Beatles.
In 2256 on the USS Discovery, when Paul Stamets was expecting to receive a Vulcan in engineering, Michael Burnham (a Human), told Paul Stamets that while she wasn't Vulcan, she had been raised on Vulcan. Stamets responded that his uncle Everett was in a Beatles cover band, but that didn't make him John Lennon. (DIS: "Context Is for Kings")
According to the script of Star Trek, John Lennon, along with Paul McCartney, was the answer to the question "Identify the 20th century Earth composers of the following musical progression" in Spock's skill dome. In the finished movie, this reference was either inaudible or cut entirely; while not present in the film, the line was included in its novelization and comic adaptation.
The duo was also cited as an inspiration for the Kirk-Spock relationship by Alex Kurtzman and Roberto Orci.