There’s an interesting discussion about “Lola” on Andrew Hickey’s blog, mainly about whether or not it’s problematic in its depiction of trans people:
I’ve dreaded writing about this song, because it’s witty, clever, and one of the catchiest things Ray Davies ever wrote, but it also perpetuates some negative stereotypes about trans people. However, it also shows more respect to trans people than any other pop song I could think of
Which might just be laying too much weight on what’s largely an ironic song gently mocking a young boy having his first encounter with what I always thought was a male transvestite, what with the last line of the song being “But I know what I am I’m glad I’m a man and so is Lola”. It’s the old story of boy meets girl, boy discovers girl is also a boy, boy discovers he couldn’t care less: well, nobody’s perfect.
If you look at it unfavourably, I guess you could say that it enacts that hoary old homo and transphobic fear of straight men being “tricked” into having sex with somebody who’s “really” a man, something that used to be a staple of bad American raunch comedies (or even the Police Academy series).
But I think that’s completely missing the point of “Lola”, which is really about love conquering all, gender not mattering and becoming fluid anyway (“Girls will be boys and boys will be girls, It’s a mixed up, muddled up, shook up world except for Lola”). It’s all done with a wink and a smile, but at its heart it is accepting of trans people more than you could say it is damaging.