No it will not work unless you sign up with the LTE plan of the other carrier
If thats the case, then YES it will work if the OP comes back to America and back on AT&T....the LTE will not work overseas with a different carrierI think you guys are misreading the question. The way it sounds to me is that the OP has an AT&T phone that they've unlocked and want to take overseas to use with a locally-purchased SIM. Their concern is that after using it abroad, will it still work with LTE back in America when the AT&T SIM is reinstalled. That's how I read it. I'm not sure of the answer, but it seems to me it should work since its the SIM that hooks you to your account wherever that is and thus determines your services.
So guys, basically if my non-US carrier/sim supports 4G LTE connection, my unlocked LTE AT&T phone's LTE connection will work with the said non-US carrier/sim?