Can anyone explain these lyrics from "The Lady is a Tramp" by Frank Sinatra?

Well,it does rhyme with tramp…
I think it was just tongue in cheek ;)

Northern California tends to get cold and damp.

My sister is in Southern Cal right now, at Disneyland. She says it is cold and damp.

Would have been a trifle risque if the lyric read….“she hates California, she pisses on a lamp” Don’t you think? :¬) I too believe he took artistic licence here. Not an uncommon practice in the music industry.

A lady tramp (prostitute) goes out at night, and California is indeed cold and damp at night.

I think it’s just one more thing in the laundry list of things this tramp won’t do (or has a problem with).
She won’t go to Harlem dressed up.
She won’t come late to the theater.
All these things society “dames” do, she won’t do.
So when she’s asked about California she puts it down (for a made up reason) because the tramp is just plain contrary.

Ever been on the street, without someone to meet, nothing to eat, it ain’t no treat!
Cold and damp might be the least of her worries, Frank knew what he meant!

It’s irony, baby!