Unless BA runs a stealth LAS-JFK service in violation of US cabotage rules, OP's original sector was likely on AA/US. Nonetheless, his bag issues are with BA. As the last delivering carrier to GLA, it falls to BA to deal with the damage & loss. BA can then sort it out with other carriers if it chooses.

Thus, not worth losing sleep over who is at fault. It doesn't matter. BA is responsible and is usually decent about it all.