I have grown black seeded simpson in the heat of summer by planting it where a tree shaded it in the afternoon, but it is a leaf lettuce. Little Gem Romaine also did well in the shade.
If you don’t have natural shade you can make it using a sheet or shade fabric to keep the sun off during the hottest part of the afternoon.
Check your Bountiful garden catalog, they should have some listed for hot weather too.
“If you don’t have natural shade...”
“Little Gem Romaine also did well in the shade.”
I’ve got shade! I have ignored a long wood planter attached to one of the brick walls because practically no sun gets to the first one half of it and sun never gets to the second half. Maybe lettuce would grow there but it would still have to endure hot air, but it’s worth a try. I need to clean the dirt out of there and put fresh potting soil mix in. .
I’ll look in the BG catalog and I have a large Baker Creek Heirloom Seeds catalog. I’ll read about the Little Gem to see if it might not die in heat.