Clean it up good, lube and then shoot it. If you're happy with it, then consider refinishing.
I've had excellent results with a product called Blue Wonder. It requires a little heat to do properly. But an ordinary hair dryer is enough. Read and follow the instructions carefully. It gives a very nice and durable finish.
However, if the pitting is bad, I'd just hit it with some common cold blue and forget it. No need in trying to put a nice finish on a rough gun.