I used to grow annuals in all the planter boxes, but the last few years they have been expensive to get enough to fill the boxes nicely. So, I just put the boxes in the shed. Veggie seed is much less expensive!
I don't think that lettuce will need much depth. I have some boxes that are only about 8 inches deep. I might try some in those too.
I usually grow herbs in the two ceramic planters I have.