First, here's the mono version of "Lucy In The Sky With Diamonds":
When the pop world started going psychedelic, more commercial artists quickly followed suit. Tommy James & The Shondells started off as a brilliant garage rock singles act, with huge hits like "Hanky Panky" and "I Think We're Alone Now". Their transition to psych pop was made in 1968, when they released the huge smash "Crimson and Clover", which in my opinion is a brilliant extrapolation of Lennon's "Strawberry Fields Forever" (strawberry : crimson :: fields : clover). Their 1968 album Crimson and Clover contains, besides the title hit and the groovy "Crystal Blue Persuasion", one of my favorite attempts to copy "Lucy In The Sky With Diamonds", the absurdly silly but fun "I Am A Tangerine". Check out the lyrics!
Tommy James & The Shondells, "I Am A Tangerine" (1968):
Americans weren't the only ones smitten with Lucy in the sky. The little-known UK band Kaleidoscope (note their trippy name, shared with at least two other psychedelic bands) named their first album Tangerine Dream, as good a description of Lennon's song as can be made in two words. Their 1967 album may or may not have given the more famous German electronic band its name, but this rare album is a gem of melodic, Beatlesy psychedelic pop.
From 1967's Tangerine Dream, here's Kaleidoscope's "Flight From Ashiya", replete with Lennonesque lyrics (e.g., "Puffs of white cotton passing the window", "One minute high, the next minute low":