To me the skin looks nice and smooth and healthy, not traumatised or irritated, so my guess would be a moult rather than lice or pecking.
Is she actually thin or is it just that she looks thin? Have you body condition scored her? It might be useful to start weighing her weekly to keep a check on it. It may be that she just looks thin because of the moult. She has probably lost feathers in other areas as well as this patch, which will make her look less bulky. Extra protein feed or treats like meal worms or scrambled egg or meat scraps or fish will help her regrow her feathers and gain weight, especially if she is continuing to lay. Making new feathers takes protein, as does egg laying. Most hens slow down or stop laying whilst they moult, so continuing to do both will take it's toll on her body if she is not getting enough protein.
I appreciate that she is young to be moulting but some hens have a different schedule to the majority and it is just normal for them to be different! If she is acting happy and normal, I would monitor and up her protein intake, but not worry unduly.