“A song like ‘Got to Get You Into My Life’, that’s directly about pot, although everyone missed it at the time … Day Tripper”, he says, “that’s one about acid. ‘Lucy in the Sky,’ that’s pretty obvious. There’s others that make subtle hints about drugs, but, you know, it’s easy to overestimate the influence of drugs on the Beatles’ music.”
– Paul McCartney (Weekly Standard, 2004)

The Beatles – Lucy In The Sky With Diamonds:

John Lennon: , lead guitar and vocals
Paul McCartney: backing vocals, Lowrey organ and bass
George Harrison: backing vocals, lead guitar, acoustic guitar and tambura
Ringo Starr: drums and maracas

The song has the distinction of being the first Beatles recording to be referenced by the group themselves: the second verse of Lennon’s “I Am the Walrus”, released on Magical Mystery Tour at the end of 1967, contains the lyric “see how they fly, like Lucy in the sky, see how they run…”

“Lucy…” was one of the fastest rehearsal/recordings for Sgt. Pepper.

The Beatles spent an 8-hour night session (28 February 1967) rehearsing the song, they didn’t record that night.The next day (March 1, 1967), they did seven takes. They laid down the rhythm track: piano, acoustic guitar, organ, drums and maracas. John Lennon sang the lead vocals  without a microphone to help with the recording of the instrumental track. Take 7 had the tambura, the Indian instrument. The day after, on 2 March John did the lead vocals, and Paul did his harmony backing. They both double tracked their vocals, and then Paul’s bass and George’s guitar were added.

“Lucy in the Sky With Diamonds” was one of the best songs on the Beatles’ famous Sgt. Pepper album, and one of the classic songs of psychedelia as a whole. There are few other songs that so successfully evoke a dream world, in both the sonic textures and words.
– Richie Unterberger (Allmusic)

The Beatles – Lucy In The Sky With Diamonds (Love album version), full intro (actually the end of the previous track). The slow build-up of organ, then drums, then bass really makes this version stand-out:

“I showed up at John’s house and he had a drawing Julian had done at school with the title ‘Lucy In The Sky With Diamonds’ above it. Then we went up to his music room and wrote the song, swapping psychedelic suggestions as we went. I remember coming up with ‘cellophane flowers’ and ‘newspaper taxis’ and John answered with things like ‘kaleidoscope eyes’ and ‘looking glass ties’. We never noticed the LSD initial until it was pointed out later – by which point people didn’t believe us.”
– Paul McCartney (Anthology)

Lucy O’Donnell, the girl who gave name to Lucy in the sky,  attended Heath House, a nursery school, with Julian . She didn’t realize she had been immortalized in a Beatles song until she was 13.

There were plenty of rumors about Lucy in the Sky with Diamonds being a song about drugs. John Lennon had discounted this theory many times, but this is an interview with Dick Cavett where he addresses the question directly

John Lennon Explaining Lucy in the Sky with Diamonds:

“The images were from Alice In Wonderland. It was Alice in the boat. She is buying an egg and it turns into Humpty-Dumpty. The woman serving in the shop turns into a sheep, and the next minute they are rowing in a rowing boat somewhere and I was visualising that. There was also the image of the female who would someday come save me – a ‘girl with kaleidoscope eyes’ who would come out of the sky. It turned out to be Yoko, though I hadn’t met Yoko yet. So maybe it should be Yoko In The Sky With Diamonds.It was purely unconscious that it came out to be LSD. Until somebody pointed it out, I never even thought of it. I mean, who would ever bother to look at initials of a title? It’s not an acid song. The imagery was Alice in the boat. And also the image of this female who would come and save me – this secret love that was going to come one day. So it turned out to be Yoko, though, and I hadn’t met Yoko then. But she was my imaginary girl that we all have.”
– John Lennon (1980)

Lucy in the sky with diamonds (Lyrics):

Picture yourself in a boat on a river,
With tangerine trees and marmalade skies
Somebody calls you, you answer quite slowly,
A girl with kaleidoscope eyes.

Cellophane flowers of yellow and green,
Towering over your head.
Look for the girl with the sun in her eyes,
And she’s gone.

Lucy in the sky with diamonds
Lucy in the sky with diamonds
Lucy in the sky with diamonds
Ahh…

Follow her down to a bridge by a fountain
Where rocking horse people eat marshmellow pies,
Everyone smiles as you drift past the flowers,
That grow so incredibly high.

Newspaper taxis appear on the shore,
Waiting to take you away.
Climb in the back with your head in the clouds,
And you’re gone.

Lucy in the sky with diamonds
Lucy in the sky with diamonds
Lucy in the sky with diamonds
Ahh…

Picture yourself on a train in a station,
With plasticine porters with looking glass ties,
Suddenly someone is there at the turnstyle,
The girl with the kaleidoscope eyes.

Lucy in the sky with diamonds
Lucy in the sky with diamonds
Lucy in the sky with diamonds
Ahh…

Check out the list so far 

Egil & Hallgeir