According to this article, it turns out that the song is not about LSD but about a child’s drawing. From the article:
Thus the meaning of this song is rather abstract, but Lennon was adamant about the meaning of “Lucy in the Sky with Diamonds” during his life. Lennon repeatedly expressed that this song was about a drawing that his young son, Julian, created while in school. Julian had drawn one of his schoolmates and friends, Lucy O’Donnell, among a smattering of stars. And when he showed his father the picture after school, he told the elder Lennon that it was “Lucy in the sky with diamonds.”
Inspired by his son, Lennon got to work creating a sonic picture of his son’s drawing. Lennon gave Lucy a story and animated her in a fantastical, whimsical story.
It goes on to say:
Soon after its release, there was a widely held belief that “Lucy in the Sky with Diamonds” was a song about the hallucinogenic drug LSD… Lennon, however, adamantly disagreed with his fans. “It never was [about LSD] and nobody believes me,” he said in a 1971 interview.
I’ve run into the sort of person who will shout with adamantine certainty that the song most certainly is about drugs. To this sort of person everything that they like is really about drugs, probably because drugs are nearly the only thing that they like. It goes deeper than this, though; this sort of person desperately wants to affirm that society—or at least the good parts of society—agrees with them.
These sort of people never actually need the song to say anything about their idol, merely mentioning it is enough for them. (This is often necessary in order to make their drug-interpretation fit the song they’re talking about; since they are imputing the drug interpretation there’s no substance there.) It makes sense, though, that these sort of people don’t require that a song actually say anything about the drugs. They are intellectually dead, which is the easiest step to take on the path to their goal—to leave this world. They’re not suicidal (for the most part) in the traditional sense of the word, but they fundamentally don’t want to be here.
There are two things that human beings are given to do in this world, and one of them will persist in heaven. The one that will persist is to love God and enjoy His goodness. The other thing, the temporary thing, is to take part with God in His act of creation. These are what are often called doing good or “good works”, and in our fallen state people often think that they are incompatible with enjoying God’s goodness. (It is hardest to do both at the same time when one misunderstands the cooperation with God in the act of creation as some sort of requirement, rather than a privilege, or worse as the price of getting something good.)
People who really like drugs want to avoid that second thing we’re given to do in this world. They don’t want to take part in creation, they just want to skip straight to heaven. Drugs are, in general, a chemical lie which allow us to fool ourselves into thinking that we’re already in heaven. This is why (with exceptions) people on drugs don’t accomplish anything (while they’re on drugs). This is also why people who regularly take drugs rarely accomplish much when they’re not taking the drugs. At a fundamental level, they don’t want to be here.
It would be bad enough if these people killed themselves slowly, as G.K. Chesterton put it “using the tools of pleasure, not the tools of pain”, but it is worse than that. Like all idol worshipers, they are not content to privately worship their idol. They want everyone else to worship with them. So they go around insisting that everyone interpret art as badly as they do, that is, they go around trying to ruin it for everyone else. They try to talk others out of wanting to be here, too. Their saving grace is that they’re horribly unattractive. After high school, one pretty much never has to interact with them again.
Except occasionally in comments on the internet.