Horses get lice when they are in poor health or are getting inadequate nutrition, particularly Vitamin A. You cannot give a healthy horse lice. The same is true of Rain Rot. You cannot give it to a horse with adequate Vitamin A in their diet.
You can use 5% Sevin Dust to kill the lice, But they will just come right back unless you get the horse in better condition. Sevin Dust comes in little shaker cans or you can put some in an old sock and pat the horse all over with it. You need to especially get the mane and top-line of the horse.
Then, the quickest way to correct the Vitamin A deficiency is to get a 100cc bottle of injectable Vitamin A sold for cattle at a livestock supply store like Tractor Supply or a Catalog from Jeffers or Valley Vet or ????
DO NOT give your horse a shot. It is made for cattle and can get a reaction. But, you can give a horse 5cc in his mouth just like a paste dewormer. 5cc a week for 2 or 3 weeks and then 5cc a month after that will get a horse started on the right track.
Then, I would feed a Vitamin Supplement that has a high level of Vitamin A. Farmam makes one called 'Mare Plus' that is very good.
Vitamin A deficiencies are responsible for many problems like: Rain Rot, lice, runny goopy eyes, scaly scruffy skin, breeding problems, mares that do not drop their placenta in a timely manner, and many more things.
Getting your mare on a good diet that includes a good supplement will keep the lice away and do a lot for her general health and condition.