That song is the first thing that went through my mind, too. It's an interesting re-framing of the song, even if there's nothing to it.
There's nothing in the Wikipedia entry that contradicts the possibility, though. Both could be true, with illicit details elided from the official telling.
Still I'm choosing to believe in innocent origins.
That's true but at least we have a bit more to go on there (if not specifically about Lucy in the Sky) - I can't dig up the original reference but it's a famous enough story to paste from a random google search result:
John told Derek Taylor that when he and Paul dropped acid together they “just stared into each other’s eyes saying ‘I know, man’ and laughing”
There's nothing in the Wikipedia entry that contradicts the possibility, though. Both could be true, with illicit details elided from the official telling.
Still I'm choosing to believe in innocent origins.