is there a locker where we can store four large suitcases and carry-on luggage?

Due to Transportation Security Administration (TSA) heightened security requirements, all lockers and storage unit use has been suspended. It may be possible to check in early with your airline, please see the ticket agent when you arrive. The above information is from San Diego International Airport official website.

Check In as early as you can. This should be the best way.

I don't think that there are any locker arrangements for baggage at San Diego airport.

Those have to be checked in at your airline.

I heard you can ask the baggage claim people