Lettuce does best in the spring, how close is your house to providing spring like conditions? Cool moist temperatures with lots of sunshine provides the rapid growth for lettuce. Difficult to provide indoors, but any leaf lettuce would do as well. Al

We grew it inside last year, too. The lettuce was tender & tasty cut as baby lettuce several times. We reused the clear container from purchased lettuce as described in the link. It was easy to harvest with scissors & very clean!

lights: just put it on top of stove to use the range hood CFL (stacked containers to adjust height) It was easy to adjust height of containers to keep leaves close to bulb. My family adapted well to the routine to remove it during the day & return for bright light at night.

Grew lanky still, so our method isn't perfected. I think it may have needed a liquid fertilizer more often. Since it was in clear sight it didn't get a chance to dry out.

Here are my notes from the article I've put in the link.

Lettuce Inside Notes:
Lettuce grows best indoors when the temperature is between 40 and 65 degrees and when it receives 6 to 10 hours of bright sunlight daily. Consider purchasing lights designed specifically for plant growing if your room does not receive sufficient light. Select a container at least 10 to 12 inches deep to accommodate deep roots.

soil:
Mix equal parts potting soil, vermiculite, peat and perlite and place into your container. Place your lettuce seeds in 1/8-inch deep and cover with soil mixture. Add water until the soil is soaked.

thinning:
Germination should take place after one to two weeks, at which time you will need to thin your lettuce to give it enough room to grow. You will need to remove extra seedlings so there is one seedling every 6 inches

watering & fertilizing (I would use worm or compost tea)
Add a mixture of balanced fertilizer that is equal parts nitrogen, phosphorus and potassium every two weeks.
Water the lettuce as often as necessary to keep the soil moist without being fully wet.

harvesting:
when leaves large enough to pull away or use scissors to cut & it will grow again

Here is a link that might be useful: Lettuce indoors