This site covers the original British Beatles Albums plus analyses of the lyrics of non-album tracks.
Information on how the Beatles wrote the lyrics to their songs on The Beatles (white album) can be navigated from below the album cover.
Beatles Album: The Beatles AKA The White Album : Track 15
Lyrics: Lennon, McCartney
The lyrics to why don't we do it in the road were written by Paul McCartney and the risque lyrics were somewhat inspired by the style of john Lennon.
John Lennon: Did not play on why don't we do it in the road.
Paul McCartney: Vocals, lead guitar, bass guitar, Piano, Drums
George Harrison: Did not play on this song
Ringo Starr: Did not play on this Beatles song