The clumps are most likely eggs (lice eggs). Lice can lay several hundred eggs, resulting in the clumps. The clumps are almost nastier than the lice themselves...
We picked up a little rooster who had lice. I saw the lice (actually only saw one, but I'm sure its buddies were hanging around somewhere) first...started scratching my head a lot. Not until the next day did I find the nest clumps...YUCK!!! And they were on there like concrete!!
Here's what I did (do a search...you'll find lots of ways to treat): I'm not good with powders. I can sprinkled DE around (many use 7Dust) the coop, but have a horrible time dousing a chicken while protecting its face area, and end up with more on me than on the bird. So I used Adams Flea/Tick spray (which also treats lice, etc.). It was so much easier to spray under the wings and around the butt while covering the face. I also spray a bunch into the hands and worked that around the neck area (be sure to get it on the skin, not just the feathers). You will have to repeat in 10 days, in case eggs hatch and survive.
We ended up cutting the egg sacks out (used tiny, sharp sewing scissors), because nothing else was working for me. I think the nit nests were dead, but hated to see them hanging there. Although I didn't see any more lice on the roo, we still treated him again at the 10 day mark, just to be sure.
I would replace bedding, and liberally mix in DE or 7 dust. Good luck!
Oh...and unless they are just COVERED in lice, I doubt that is why egg production has dropped off. I would think the heat or molting would more likely be the cause...