Do hens still nest when they are going through a hard molt?

[The_Flock]

Hi peeps. I have a Golden Laced Wyandotte, Dottie who's about 3 yrs old. She's going through a hard molt right now and she's going into nesting box after nesting box, looking for the right one. She's nesting in one right now, been in there for about 40 minutes so far. I'm pretty sure she laid a thin shelled egg about a week ago. She was already well into her molt at this time. It's pretty cold here right now and that egg broke under the pressure of me picking it up.
Almost all of my chickens are going through a hard molt so I'm feeding them mashed hard boiled egg, sesame seeds (which they seem to get runny poops from), pumpkin seeds (they're not too keen on these), dried mealworms, kale, dandelion leaf, appropriate meaty leftovers, oatmeal (sometimes with yogurt), rice crispies cereal, as well as their regular feed. I feed them the eggs everyday and give them varying other sources of protein throughout the week. Dottie is 3rd in command and is always right there with the yummy food. They have heated water bowls and I put ACV in there about 2-3 times per week. They are staying inside because of the snow. I put a coop rated heater in one of the nesting boxes because ono of our Golden girls went through a hard molt last year in an unseasonably and incredibly cold late fall.
I just can't figure out why Dottie is laying sometimes still and nesting everyday. Her comb and wattle are very red.
Oh also I spotted many lice on one of my girls. I'm not sure about mites but I'm assuming we have them. So I did treat them for that with ivermectin wet spray in a cold time of year. This was vet recommended. I heated the coop just a bit so they weren't freezing AND wet. They all got through it very well.
Any help you guys can offer is awesome. Thanks in advance and have a great day.

 

[Ridgerunner]

In the "normal" scheme of things, chickens in the wild that forage for their food stop laying in the fall and use what food they can find to molt and grow new feathers. But we've domesticated them and bred them to lay a lot more eggs than "normal". Plus many people feed them a much richer diet than they can typically find in the wild. Some even provide heat. Some hens get extra light, either on purpose or from street or security lights. So, yes, some hens will lay an egg when molting.

 

[The_Flock]

@Ridgerunner that makes sense. Thank you. About the light, we live on a rural but busy-ish intersection and at night the headlights shine right at the coop when ppl stop at the stop sign in front of our house. I've always felt that the girls were getting affected by it.