you will have to go thru US custom despite doing just an international to international connection. You need to claim your bag even if the bag is tagged to your final destination. You will have access to your bag at LAX. If your bag is tagged to final destination, usually all you need to do is do a bag drop after custom. If bag drop service is not available after custom, you will need to haul the bag to AC check in counter to drop the bag. If not tagged to final destination, you need to recheck the bag at AC counter.

I don't know about flights departing from ICN, some airports perform liquid control just before boarding near the gate for US bound flight. Some no duty free/liquids under those circumstances.