What kind of doctor would perform neurolysis of the obturator nerve? Orthopedic or neurosurgeon?

Orthopedic surgeon. This diagnosis and surgical treatment best undertaken by an orthopdic speialist who deals with hip reconstruction and pelvic/acetabular fractures.
Neurolysis? That's a strange procedure. I've never heard of obturator nerve entrapment that requires release and neurolysis. I might get a second opinion.