A FOX Savage Arms Corportation Double 16 gauge shotgun was given to me by a family member...and it looks to have a problem.

I not sure of the problem, but the "lever" used to open the action does not come back to center (stays to left side and springs back to the left when moved to the right or center) at all times...

Any suggestions? Is it worth repairing?

Typically that lever has a wear factor in it. When new it should stop just slightly right of center and as it wears in it's lifetime it'll move more to the left. Apparantly your gun is a bit worn in the closing locks.

If the barrels are firmly attached to the boxlock...meaning when the action is closed the barrels don't wiggle up-down then I'd not hesitate to use it.

In time the barrels will wiggle and the lock needs to be repaired.

One of the things that cause short life with these guns is to not slam the barrels close. Close them firmly but gently and they will last a very long time.

If the barrels wiggle up-down with the action closed I'd take it to a smith to be repaired.