I used to plant Pyrethrum daisies (Pyrethrum Daisy (Tanacetum cinerariifolium)
) amongst my Brassicas. If you have problems with Cabbage Whites, the flowers will act as a deterrent to them. Marigolds are also a good pest-deterrent generally, but I'm not sure if they help with Cabbage Whites specifically.
Lettuce would probably be OK as an edible companion - the shade from the taller plant won't bother it at all, and you can harvest it without affecting the sprouts. I wouldn't plant a root crop like beets there for two reasons: sprouts like a firmly packed soil while root crops need it lighter, and you would disturb the roots of the sprouts if you try to harvest any beets before it's ready.