...making this for a lactose-intolerant friend, how can i replace all the milk, butter, etc? (she can have goat cheese!)

You should ask your friend if she can have hard aged cheeses, or sheep cheese, often lactose intolerant people can have parmesan cheese because the lactose in it is almost non-existent, but Pecorino-romano is a very similar in flavor and is made with sheep milk rather than cow (if goat is okay, sheep generally is too).
I would use broth instead of milk, sub olive oil or coconut oil for the butter, and maybe a nice dollop of fresh goat cheese on top.

Both suggestions given sound good. I might ask your friend if she tends to use almond milk or rice milk and if she likes them - if so then put that in the polenta; if not it would be great with just stock.

Since you can't use the cheese of the creme fraiche, I would drizzle a bit of good quality olive oil over the top to add some tastiness.

Butter has very little lactose--and none if you clarify it--so you're ok to use it. I would make the polenta with stock only because I don't care for almond or rice milk, but that's just me.

I would bring the stock only to a boil and infuse that, then pour in a cup of unsweetened almond or rice milk and bring that to a bare simmer with the stock. I've used it in polenta before and it turned out just fine. For the butter, you could use Earth Balance.