Hi there, hope you are enjoying BYC!
I'm gonna start by saying molting birds DON'T lay eggs usually as all their energy is going to regrowing feathers.
Next.. what is your location? I know there are different standards of perfection by country.. but that is NOT a purebred Araucana.. They would not be crested as your girl is. In the US Araucana are rump-less.. and tufted.. different than beards and muffs.
Her feathers do look like heck.. not uncommon in birds that need to molt soon.. and lavender feathers can be more fragile than others.
Honestly.. she doesn't look like she's molting to me. Her feathers won't improve until she does molt.
Signs of lice or mites would be angry red skin below the vent and on the abdomen.
The point trying to be made by the other poster about using a flock raiser feed.. is that most layer feed are 16% protein which is considered the MINIMUM to maintain a light bodied layer like Leghorn in good condition. Most treats folks feed actually diminish nutrients not enhance them.
You gal is looking more dual purpose shaped in her body.. AND feathers are made from 90% protein and it's amino acids. Also molting birds don't lay and bird NOT in lay should not be fed calcium in excess of 3% long term as it *could* cause gout, and kidney issues.. including failure and even sudden death.. Most likely in those genetically predisposed somehow. Most layer feed has at least 4% calcium. I never ever feed layer since learning the difference and my bird have softer molts and return to lay sooner since making the switch a few year back. Oyster shell is free choice on the side for active layers. The more amino acids also work to support the overall immune system including fighting off internal and external parasites. Plain dirt is great for a dust bath.. each bird has their own routine, some bathe more than others.
Even though she doesn't appear to be molting to me.. I have had them randomly take breaks from laying.. especially after a change in environment like a move. Make sure she isn't hiding a nest somewhere. And beyond that.. wonder if she was being sold because she wasn't a good layer..
Adding your general location to your profile can help folks make their most relevant suggestions possible at a glance.
She is beautiful, glad she's settled in nicely!