I think "Lies" by the Knickerbockers is hands-down the best Beatles sound-alike track I've ever heard. IMO, those guys captured not only the sound of the Beatles but the essence of the group as well (around the 1965 timeframe).
Of course, the Rutles did a fantastic job as well - in fact, I think they did the Beatles even better than the Beatles!!! - Don't you think? (wink, wink)
Another track that always sounds Beatle-esque to me is "Wonderful World" (Sam Cooke's song, not Satchmo's) by Hermin's Hermits - not as much Peter Noone's vocals but the music sounds like it came straight off one of the Fabs early Lps.
As for a Lennon-esque tune, I thought "Pop Muzik" by M was John when it was first released in the late '70s. The mystery performer known only as "M", the irreverent wordplay, the cryptic references to his former bandmates' songs "try some, buy some" and "Get Back", the female backing vocalist whose voice sounds like it could be Yoko, etc., had me convinced it was John's anonymous tongue-in-cheek attempt at a comeback. NOTE: I never saw the video for this song until Youtube. If you listen without seeing the video even you might think it could be John!