The song's "the Walrus was Paul" lyric is both a reference to "I Am the Walrus" and Lennon saying "something nice to Paul" in response to changes in their relationship at that time. Later, the line was interpreted as a "clue" in the "Paul is dead" urban legend that alleged McCartney died in 1966 during the recording of Sgt. Pepper's Lonely Hearts Club Band and was replaced by a look-alike and sound-alike. The line is preceded with "Well, here's another clue for you all".
Lennon himself dismissed any deep meaning to the mysterious lyrics:
I threw the line in—'the Walrus was Paul'—just to confuse everybody a bit more. It could have been 'The fox terrier is Paul.' I mean, it's just a bit of poetry. I was having a laugh because there'd been so much gobbledygook about Pepper—play it backwards and you stand on your head and all that.