No need to squat in a locker you don't own, it may become not your stuff.

If the reason for this survival situation is a bad earthquake, expect lots of broken stuff like windows. A pair of hiking boots will do a better job protecting your feet than running shoes and a pair of gloves will be good for keeping your hands from getting sliced. A small radio will be useful to get information regarding earthquake damage. That said, La Jolla is 90 miles from San Andreas, no where near as close as Philip(<5 miles), and probably not close enough to do massive destruction to San Diego/La Jolla. Still, it's always good to be prepared.

Under the assumption that you will be staying near the school until someone picks you up, keep a backpack with water and protein/energy bars/trail mix to keep you moving, an LED flashlight with extra batteries, a small first aid kit to include a couple N95 masks. For a longer term event (this is where the spare locker would be nice), a sleeping bag/blanket and change of clothes (heavy duty) would be good to have available. Hiking/camping gear would be very useful.

My suggestion would be to discuss this with your parents and have them ask the school what supplies they store in case of a serious earthquake/other natural disaster requiring them to keep the students at school. Since it's a private school they may be more open to students making personnel preps and may provide storage (that way the spare locker will be yours).