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What sort of lights are you using? Some details about your growing setup might help diagnose the problem.

I grew some yummy salad lettuce under fluorescent lights. Tips: Keep the tops of the plants close to the lights; harvest a few young leaves (4" long or less) frequently rather than waiting for mature heads to form; keep them cool and well-ventilated; feed with a balanced organic fertilizer. I grew mine in clay pots, which may have helped keep the roots cool and aerated, and had the lights on about 16 hours per day.

If all else fails, you could try a different variety of lettuce. Try sowing some that's sold for "cutting."

Some varieties - green oakleaf and "speckles" tend to be very limp...