You have 3 authority levels to comply, TSA, airline, and local. But no special lock required, if the OP lock functions that would be fine. Minimally the airlines must meet the TSA guidelines but they can go beyond. Traditionally none of the US carriers have gone beyond but I "think" Southwest recently announced no ammo in the case. But you always check your specific carriers. Intl carriers absolutely must be checked as there is an array of special regs like attaching paperwork to the case, counting number of loaded and unloaded rounds, no ammo in case, etc.
For example of the 3 levels, TSA says you can put the ammo in the locked gun case, American, Delta, United says you can put the ammo in the locked case (maybe not Southwest}. Local, JFK says no ammo in the locked case. So if you check with TSA and United and decide to put the the ammo in the case but you are flying in or out of JFK you could be arrested in JFK for carrying a loaded firearm, ammo in a locked gun case is defined there as a loaded firearm, ask me how I know.
From TSA:
You may use any brand or type of lock to secure your firearm case, including TSA-recognized locks.