I doubt you need a permit. Even with my bath remodel where a new electrical line was installed to provide the code required dedicated 20 amp line there was not a permit required and I used a licensed electrician.
The carpenter who builds out the cabinet is not the same person who should be running the lights for the closet. For a walk-in closet I would want lights but for a regular depth wall closet a light is not essential.
The closet lights can use the same leg that is supplying the ceiling lights in the room now and add a switch or switches for the closet. If there is access from above in the attic then this is a trivial job as the electrician can run Romex from the ceiling light box to the new boxes for the closet ceiling lights.
For any work a contractor will ask whether you plan to pull permits. When I have said I was not going to get permits I have never had a contractor turn down the job regardless of the scope with the exception of roofing and solar installations. I added a natural gas feed standby generator and it was put in without permits but I did use a licensed electrician and a licensed and certified plumber.
Good idea to go to the website for the local building and permit department as it will specify what work does and does not require a permit.
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