This is somewhat risky, especially at LAX which has a big CBP presence. Generally, TSA does not look for visas, but as others have mentioned, they could if they wanted to.
One way around it is to start your trip at a domestic airport. For example, you could do BUR-SFO-KOA. There is no CBP at BUR and therefore it's incredibly unlikely that TSA there will do anything. Another suggesetion is to go when it's crowded. The longer the line behind you, the less they will pay attention.
Also, it is important to dress and act appropriately. TSA does stereotype, despite what anyone claims. If you don't make eye contact, are dressed shabbily, and avoid answering questions, they are more likely to scrutinize you carefully.
Is this person eligible for DACA? If so, he/she can get an acceptable state ID that can be used. Otherwise, I would not bring the ID (or the receipt) to the airport.