I tried ivomec (which I have heard can work) when my goats had lice but for my goats it just didn't work so I used a cattle lice treatment (forget the name) that wiped the lice out by the next day. they only needed a little applied to the back of their necks.
I have also heard that rubbing sulfur into their coats works well. Some people also add 1 tsp of sulfur per goat to their feed to keep lice away.