The thing is, it very much *won't* be random numbers. It's about as far from a random number generator as you can get.
In a really bad model, one would expect it to likely be "numbers it's seen the most in the context of a lottery". But in a good model, esp. a thinking model, one would expect it to think over which sorts of numbers are statistically over-chosen (birthdates, etc) and avoid them in giving its answers.
The funny thing is, think of how this woman will interact with ChatGPT from now on. ChatGPT could say "Abraham Lincoln was married to John Wilkes Booth", and she'd be thinking, "Okay, that sounds really, really wrong, but on the other hand, it picked the right lottery numbers, so..."