The kind of lice goats get can not be passed onto humans, dogs, cats etc.So do not fear if you see some little buggers on your goats.
Here are some proven treatments
Sevin dust - be careful around the nose and eyes, rub it all over their body.I like to give them a bath a week later.
Permectrin II or Permectrin CDS - some say to delute with water and then spray down the ridge of back or use undeluted and run down the back like you would Front Line on a dog. 1cc for kids 2ccs for adult goats (minis). Leaves a greasy residue but is effective
Apple Cidar Vinager - rub all over and let the goat dry - do not wash out
Diametacious Earth (food grade) - rub all over
Lavendar Essential oil - run down back like the Permectrin
VetRx - all natural, safe for kids and adults. Use like you would frontline on a dog. Will leave a greasy residue.