There is a significant amount of literature about lettuce cultivars (cultivated varieties) that do well in the summer heat.
One paper out of Auburn University (in SOUTHERN Alabama) states
Cultivars ‘Aerostar’, ‘Monte Carlo’, ‘Nevada’, ‘Parris Island’, ‘Rex’, ‘Salvius’, and ‘Sparx’ performed well in a hot greenhouse and were preferred by consumers (for flavor).
Another paper out of Purdue (southern Indiana) states that the following varieties are suitable for summer harvest
Bibb: Bambi, Deer Tongue (specialty)
Butterhead: Adriana, Nancy, Pirat, maybe Sylvesta.
Leaf: Tropicana, Panisse (specialty), Green Star.
Romaine: Aerostar, Coastal Star, Freckles (specialty), Green Forest, Green Towers,
Salvius. Summer Crisp: Nevada.
with Green Forest head-and-shoulders above the others in terms of marketable weights.
Winter lettuce differs from summer-lettuce cultivars because the newer, day-neutral cultivars that do well in the summer are daylength neutral. They tend to bolt at 65 days regardless of heat units and daylength (although drought can tip them into early bolting). All lettuce becomes bitter when it bolts.
The issue with fall and winter is that the plant grows slowly and will be tiny at 60 days. One could plant thickly and harvest as mini-greens but the leaves can be little-fiddly things to wash.
Older cultivars without the daylength-neutral genes will hold for 112 days (or more) without bolting under six hours of light a day which allows them to both size-up more and to "hold" in the greenhouse bed until the cook is ready to harvest them.
Unfortunately, sellers of lettuce seeds do not specify whether varieties marketed as "winter" lettuces have or do-not-have the daylength-neutral genes. Lettuces like "Winter Density" and "Rouge D'Hiver" have names that imply that they do well in the late-fall and winter but words are cheap.
What do you guys with greenhouses (Howard? Anybody else?) have to say about lettuce cultivars to stretch out the season into the short days of fall and winter? Any favorites?