I think it's pretty permanent once it shows up. I've had seasons where all I catch have lice. It seems as lately there have been more healthy wolves taken.
Coyotes had it commonly for a while but I don't trap as many of them as I used to so it's hard to say if they have improved.
Many years back my Golden ret. picked lice up from the coyotes in the neighborhood, I wasn't trapping then. Ivermectin works great if your dog gets them. All the years of skinning lousy wolves my dogs have never picked them up oddly enough.
Something else I've learned is that the leather does not tan up that great on wolves with lice. Has to do with the oil the skin is secreting to combat the lice making the leather tan up cardboard like. Also the underfur starts to matt up in the areas where there is still guard hair. The root beer color is common with most canines I believe when they have allergies or parasites. You will see it in the groin, feet, and under the muzzle. I used to sell the salvageable ones, but now I just take the skull, and claws if they are nice and leave the rest in the bush.
These are just my observations I'm no expert, and I could be very off base on any of that.
Here are a few nasty ones, and some that look decent, but weren't worth skinning