Student or Learner
Would this expression be standard "to bust one's lady balls"? Is it similar in meaning to "to bust one's balls"?
No, it's not standard, but you understand what is being said. It's an attempt to be clever.
It's new to me, but I quite like it.
It might relate to a Little Britain skit about one Eddie Howard pretending to be a Victorian lady and having 'small lady testicles'.
I don't think this is a common slang term.