The word "illusion" already describes a false sense of reality. That is why magicians are said to do 'illusions' with their magic tricks. Another term might be mirage as in a desert mirage.
The Beatles songs are great because their lyrics combine wit, wisdom, fun, depth and transcendence like Lucy in the sky with diamonds walking the yellow marmalade road. This, together with the same for their music which had many moods and registers. They didn't follow fashion - but made it. And their songs remain timeless which is why they are, and will always be, perennial and evergreen favourites.
When their words don't make "sense" as you put it, this is because they were using their words as yet another musical instrument. After all, do musical instruments make "sense" as words? No, of course not. But this is because they resonate with the heart and not the head.