Generally speaking, leafy vegetables are the most shade tolerant eg:
Cabbage
Chard
Kale
Lettuce (which you already mentioned in your question)
Spinach
But if you've also had success with root vegetables (carrots & potatoes), you could try some other root vegetables eg:
Beetroot
Onion (not a true root vegetable, but a bulb vegetable that should do ok! in your situation)
Parsnip
Radish
Sweet Potato
Turnip
Below, I've gathered together some relevant reading that I believe you will find helpful/useful: