You have to leave the eggs - dust him again in 7 days and again. You can also use adams flea and tick mist (on a paper towel) in some areas.
Are they wheat colored, or blood-taking grey with possibly black bottoms? A good bath could help, too.
Nothing kills the eggs, but the repeated dusting kills the lice as they emerge.
I agree with not using the ivermectin yet. Especially if he's in that sort of shape. After you get the lice off, you could use a piperazine wormer - a gentle one (do you have that there?). Then in 2-4 weeks you could go back with a stronger wormer.
The white sticky stuff are lice eggs. Did you see any bugs on him? Mites are round, lice are longer like the lowercase letter L. Mites lay their eggs in the wood of coops and will leave the bird and go there - so look for the literal lice. They like feather shafts, particularly in the 'wing pits' and under the feathers there.
Poor guy! I'm so sorry you're facing this. I do hope you're keeping him quarantined; both for his sake, and your own birds. He has to have a crappy immune system.
You can give him yogurt to keep his digestive tract running well during this transition period (change in living area, change in food, probably a change in the *quality* of food, stress of being exposed to new 'bugs', etc). I'd give him vitamins/minerals in the water, and if you have a package for poultry there that includes electrolytes I'd give that too. Just the standard water treatment. Then keep him isolated, feed that boy up, maybe work in a week once the lice are settled down.
Poor little guy - and little pekin roos are just the dearest boys, too! I hope he comes through his quarantine well and does awesome for you!
p.s. I once bought a bird off of an online selling site - a crele OEGB cockerel. His picture was definitely acceptable, a nice bird. However when I got him I found him much in the same condition as your pekin. Only it was mites, not lice, and he was covered with them. The droppings were all over his tail, crusted in balls under his toes, he had scaley leg, and despite my best efforts he just simply died. It was so depressing, the poor little guy. He was so lovely and it broke my heart. I don't know how anyone had the absolute audacity to sell a bird in that condition, but at least he died here with some food in his belly and no mites! He never left quarantine.