I'm with Tom as the Skillet is BS&R, and the lid is a BS&R possible.
Questions I have.
Why if you have a pattern with a handle on it, would you remove all traces of that handle, and go to a costly button handle? I am calling it costly due to having to purchase or additionally; cast a button handle, buy the bolt that holds it on, and then pay for an employee to manually apply it. That extra work/cost/time, makes me wonder why? Especially when you have DESI (automatic molding machines) patterns with a handle on them already. DESI's can turn out a mold every 15 seconds with handles already in place. Why slow down the production, having an employee sitting there screwing handles on lids as fast as he can, that is after they cool off? The other question I have is the lack of markings on the inside of the lid. The BS&R lids I have are marked with the size, either under the handle or on the underside of the lid. This style of lid dimples usually have the same markings as your skillet does on the underside.
Could BS&R have made this lid, certainly, can we prove it, no. Maybe a catalog will show up showing that type of lid, but until it does...