Spring and fall crops...

You have figured out lettuces, which should do well for you.

Peas maybe..(maybe).  Try the sugar snaps--the ones you grow for the hull and not for the mature pea--first.    

The cole crops like Broccoli have a chance, but I don't know how much light you will have.

One thing you CAN do is give bottom heat for seed germination using mats, etc , and that will help with development.  Having the roots somewhat warmer, and enough light, can go a long way toward helping plants establish.  

The guys here who have used the indoor lights for production will know far more than I do about what is possible.   For any good-tasting produce, you will need a full-spectrum light.  

Just thinking out loud, you might could do beets, but they might also stay small (which is okay--small beets are tender beets).   Radishes should do pretty well.  

@kallnojoy