Picture yourself in a boat on a river
John Lennon remarked in an interview with Playboy that this first verse was inspired by Lewis Carroll's Alice in Wonderland.
Lennon, to Playboy: "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 visualizing that." (Source)
Lennon might have gotten a bit mixed up, though; this episode actually comes from the "Wool and Water" chapter of Through the Looking Glass, which is Carroll's prequel to Alice’s Adventures in Wonderland. In the chapter, Alice walks into a shop to discover a sheep sitting behind the counter and knitting. After a few moments of conversation, the sheep asks Alice, "Do you know how to row?"
All of a sudden, the knitting needles turn into oars and Alice finds herself rowing with the sheep through a river lined by scented rushes (water plants). Alice, confused and delighted by the whole thing, starts picking the rushes. Then a crab latches its claws onto her oar and suddenly Alice and the sheep are back in the shop again. The sheep asks her what she would like to buy. Alice selects an egg which later grows into Humpty Dumpty. Interestingly, Humpty Dumpty is often thought of as the inspiration for "the eggman" in Lennon's song "I Am the Walrus."
Tangerine trees and marmalade skies
Although the songwriting on "Lucy" was a collaboration between Lennon and Paul McCartney, this line was purely Lennon's.
Many people have long suspected that this song was written to describe an acid trip. This line, along with some of the other more visually descriptive and bizarre wordplay in the next verses, seems to suggest the tracers, vivid colors, and hallucinations that can occur during a trip.
However, the Beatles all fervently denied that the song was written about LSD, except Paul who admitted to BBC news that their other song "Day Tripper" was, in fact, about the drug, and that it was "pretty obvious" that "Lucy in the Sky" was "informed" by LSD. Lennon, however, insisted that the idea for the song came to him from a drawing his son Julian brought home from school which he called "Lucy—in the sky with diamonds."
A girl with kaleidoscope eyes
John Lennon once said that "the girl with kaleidoscope eyes" was Yoko Ono.
First of all, the kaleidoscope is a popular optical toy, a hollow tube filled with mirrors set off at angles from each other and colorful beads. When the tube is rotated, you can see beautiful geometric patterns that seem to grow out from one another.
John had already met Yoko Ono when he and the rest of the Beatles went to India with the Maharishi Mahesh Yogi in 1968. Lennon was falling more and more in love with Yoko despite still being married to his first wife, Cynthia. After several months with the Maharishi, John still had not been granted the "secret" of life. He became bitter and disillusioned, and eventually left, dissatisfied with with the Maharishi in particular and with religion in general.
When he returned to the UK, his love for Ono solidified and they finally began their affair, a love story that would sweep him away from the Beatles, make international headlines, and turn the entire world (not just Cynthia) into jealous exes. Lennon realized that the secret to life he had been so desperately searching for was not a sentence, but rather a woman: Yoko Ono.
As he explained to an interviewer:
It takes time to get rid of all this garbage that I've been carrying around that was influencing the way I thought and the way I lived. It had a lot to do with Yoko, showing me that I was still possessed. I left physically when I fell in love with Yoko, but mentally it took the last ten years of struggling. I learned everything from her… [In the song] 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.' (Source)
Cellophane flowers of yellow and green
This was one of Paul McCartney's lyrical contributions to an otherwise Lennon-dominated song.
Cellophane is a type of clear, sheet material made from the cellulose (or fiber) of plants. It's used for all kinds of products from food wrappers to Scotch tape.
Towering over your head
This lyric of flowers towering reminds us a lot of Alice in Wonderland, when Alice shrinks to the size of a bug from drinking from the "Drink Me" vial.
In the movie version (which came out in 1951 from Disney) Alice drinks from the "Drink Me" vial and suddenly shrinks down so small that the flowers in the garden tower above her. The flowers begin to speak to her and then decide to sing her a song called "Golden Afternoon." In the song, the "bread-and-butter-flies," dandelions (who look like actual lions), lilies, roses, orchids, and geraniums all sing to her while she sits on a leaf and listens.
In Lewis Carroll's Alice’s Adventures in Wonderland, he includes a poem called "Golden Afternoon" but the words are quite different from the Disney song. The poem is more about Alice's adventures in general and the wild, wandering imagination of children. It ends:
Thus grew the tale of Wonderland:
Thus slowly, one by one,
Its quaint events were hammered out--
And now the tale is done,
And home we steer, a merry crew,
Beneath the setting sun.
Alice! a childish story take,
And with a gentle hand
Lay it where Childhood's dreams are twined
In Memory's mystic band,
Like pilgrim's withered wreath of flowers
Plucked in a far-off land.
Lucy in the sky with diamonds
The song's title, according to Lennon, came from a drawing that his son Julian brought home from school one day.
Lennon had one son with his first wife, Cynthia, but was rarely around to watch his child grow up. When "Lucy" was first released, the BBC banned it for supposed references to LSD, but the Beatles denied any such link.
Lennon claims that his son brought home a picture that he had drawn in school of Lucy, a classmate he had a crush on. The picture showed Lucy surrounded by a starry sky. When Lennon asked him what it was, he replied, "It's Lucy—in the sky with diamonds," and a song was born.
Rocking horse people eat marshmallow pies
Yet another startling visual which reminds us of Alice in Wonderland.
A rocking-horsefly actually appears in the third chapter of Through the Looking Glass, when Alice has a conversation with a gnat about the various insects in the forest:
'All right,' said the Gnat: 'half way up that bush, you'll see a Rocking-horse-fly, if you look. It's made entirely of wood, and gets about by swinging itself from branch to branch.'
'What does it live on?' Alice asked, with great curiosity.
'Sap and sawdust,' said the Gnat. 'Go on with the list.'
Alice looked up at the Rocking-horse-fly with great interest, and made up her mind that it must have been just repainted, it looked so bright and sticky; and then she went on.
Newspaper taxis appear on the shore
This was also Paul McCartney's lyric, and is what brings the adventure away from the countryside and back to the city.
Although "newspaper taxis" is a nonsense lyric (there is no such thing as a taxi made out of newspapers, duh), it still makes sense in a Carroll-esque sort of way.
The two strong images "newspaper" and "taxi" make us think of an urban setting, a big city like New York, where these two things are everywhere. This is the part of the journey where our boat carries us downstream from some remote, magical wilderness back to civilization and a different breed of surreal lifestyle.
Climb in the back with your head in the clouds
Although all the members of the band furiously denied that the song had anything to do with drugs, this line suggests otherwise.
Acid trips are often described by users as "out of body" experiences in which they lose touch with the physical reality around them and seem to be floating in space. Colors are brighter, everything blurs, lifeless objects start to move and ripple, and you feel as though you're drifting away.
Having one's "head in the clouds" refers to somebody who is spaced-out and oblivious to the world around them. This could just refer to someone who is absent-minded like Mr. Magoo. It seems pretty likely, though, that the Beatles were remarking on someone who is so "incredibly high" (see previous verse) that their head feels like it's in the clouds.
With plasticine porters with looking glass ties
This line combines two ideas, one drawn from Lewis Carroll and one from a British radio comedy program.
Lennon was familiar with the British comedy troupe (including Peter Sellers) who made The Goon Show.
One of the jokes from the show mentions "plasticine ties." Plasticine is a putty-like substance used to mold figures, often in animation ("Wallace and Grommit" is a good example of plasticine animation). The "looking glass" here line is a direct reference to the title of Carroll's work.