The depth of your container is 6" and your plants are now about 5" tall, then I'd assume that they would be suffocated every time you water 'cause the container is too shallow. I would really recommend reading about perched water level in a container in one of the gardenweb forum to know more about container gardening.

You indicate you are new to gardening so I'm guessing you may be expecting lettuce to be like purchased romaine or iceberg lettuce. They will not be like that unless you grow those varieties AND grow them to a large size. That is hard to do with a set up like you describe. When young, most greens are soft and tender (limp?) especially if they are grown indoors with no wind or temperature changes to toughen them up. I find buttercrunch and romaine types grown outdoors will get a little crunch when they aren't too big, but they aren't crisp until they are larger. Other varieties, such as Black-seeded Simpson, I would never consider crisp at any size.

Maybe I'm guessing wrong here. If your leaves are much limper than the baby greens sold in stores there may be other problems. The container gardening forum may give you some suggestions and ideas. A few things I would suggest are running a fan near the plants, moving them to within an inch or two of the lights, and trying different varieties. You should be able to grow baby mesclun/lettuce in your shallow containers if they have drain holes and you don't over or under water. Also, I'd stay away from the moisture control mix. I find it difficult to keep that from being too wet much of the time.

Here is a link that might be useful: Container gardening

Thank you both for responding. Ceth_k, I admit to having read quite a lot about container gardening, and never come across "perched water." Mostly I was interested in the 5-gallon self-watering buckets, though, and it appears those are tall enough so as possibly not having the problem. This is something I'll have to test for. I have incorporated naturegirl's suggestions. Thanks again,
Dona

This may sound silly, but my container lettuce "wilts" when it needs watered. My lettuce likes lots of water, but will rot easily at the same time. So I added a bunch of perilite to the potting mix and then I just water away if the lettuce starts to droop. No rotting (or damping off of the baby sprouts). Plus my lettuce likes it kinda cool. When the sun comes out and warms up the greenhouse too much, the leaves wilt, but spring back up during the night. My lettuce is in 4.5" pots and it doesn't seem too shallow at all.

You can also try swiss chard, bok choi, and beets (for the greens) and celery (plant a bundle in a pot right from the store to make leaves and new stalks as you harvest). I've been able to make several salads so far this winter with this combo.