Mites suck blood and cause anemia and death if not treated. So yes, that could cause her to be lame, but it might not be the only possible cause. Can you get permethrin garden dust from TSC or a feed store, put some in a sock, and dust her and you other chickens all over? Permethrin ready to use spray is okay in warm weather, but they can get chilled. Coop bedding should be removed far away, and nest boxes, coop, and roosts should be sprayed with permethrin. The Martins or Gordons Permethrin 10 concentrate is economical to mix with water 1 tsp/5 ml per quart or liter of water to spray the coop. That lasts about 30 days. The chickens need to be treated once or twice more at 7 day intervals to get any newly hatched mite eggs.
The only way to know if Mareks killed a chicken is to have your state vet lab perform a necropsy and testing on the body after it dies. Keep it cold in a refrigerator or in a cooler with ice packs. Do not let it freeze. Here is a list of state vets to contact and some instructions:
https://www.metzerfarms.com/poultry-labs.ht