Our American flight has been set back so that we have 7 hours before the LA -St. Louis flight. We are flying first class. Can we use the AA lounges in LA? If so, is there food and/or showers available?

I don't think you can for a domestic first class, only international. And the food is free

Domestic first class does not grant you access to AA's lounges. If you are arriving on an international first or business class ticket on AA or a Oneworld partner you should be granted access provided you can show a copy of your boarding pass from the same day international arrival. The Flagship lounges near gate 40 have food and showers available.

You have to pay for the food

Yes, you can! And, yes, the lounge has food, drinks and showers