Definitely make sure it is a "TSA-approved" lock. All the big name lock companies make them. You should be able to find them at Lowes, Home Depot, Wal-Mart, Target, etc. If the lockis not TSA-compliant, they could call you out of the secure area to unlock it or, more likely, use a bolt cutter on them.
Actually, that's incorrect. FAA regs require it to be a lock to which only you have the key. That doesn't include all of TSA. They're required to call you back so you can unlock the gun case if they need to see inside it. You should wait near the ticket counter for about 5-10 minutes at TUL. If they haven't called your name by then, you should be good to head to your boarding gate.