I attack with 2 units, and one unit is equipped with Last Rites. I conquer, but the unit that wasn't equipped with Last Rites dies. When my Last Rites triggers on conquer, can I play the unit that died during this same combat?

Yes — the unit is already in your trash by the time Last Rites' conquer trigger is placed on the chain, so it's a legal target to play back.

Order matters, and it works in your favor here: combat damage and the deaths from it resolve in the Combat Damage Step and Combat Cleanup, before control is established and the conquer event happens (Rule 468). Since Last Rites' target is locked in at the moment the trigger is finalized and put on the chain (not at resolution), and that point comes after your other unit has hit the trash, that unit can be chosen — this is the mirror image of FAQ #11850, where the card entered the trash too late to be picked.

Two caveats: the unit equipped with Last Rites must still be alive and at the battlefield when control is established (FAQ #9015), and you still pay the played unit's full cost. You can play it to your Base or the battlefield you just conquered.