That should work.
I would treat the birds immediately. The lice can only survive up to a week off the bird so they live their entire lives including breeding, egg laying and feeding on the bird.
You'll have to retreat them anyway so I wouldn't wait for the first treatment.
No product will kill the eggs so that is why you do the 7 day retreatment.
Lice go through an entire generation in 3 weeks. One female lays up to 300 nits so one pair explodes to 120,000 in just a few months.
I would not be bathing chickens in cold weather. An exception would be if you brought them inside and blew them dry. DE is worthless for a lice infestation. The product you have is permethrin 0.25% which would be fine to dust your chickens. Repeat in 10 days to get newly hatched lice eggs before they lay eggs.
Most feed stores have Gordons or Martins permethrin 10 concentrate, that is mixed with water 1:200 to use a spray for the coop, roosts, and nest boxes when they are emptied of bedding. A small 8 ounce bottle for around $8 will make many gallons of spray to be used with a spray bottle or garden sprayer. It also can be used on chickens in warmer weather.
I usually use 5% Sevin dust which contains carbaryl as the active ingredient.
There is evidence emerging of lice resistance to permethrin. It is probably a good idea to alternate chemicals to slow the incidence of resistance.
Thank you all! I will dust tomorrow and treat again in 7 days and clean coop again. Do I need to give them another bath (I hope not but I will if I have to) I bathed each one in my garage with heater running and dried each with a towel and put them in the brooder with the heat lamp till they dried completely. It was a lot of work!