This list from MEN is one I used; however, lettuce is *not* going to grow in this heat, let alone sun. I tried. I know some people grow herbs successfully in summer, but, again, I'm not one. Good luck. It may help to tell everyone just when those 2 -3 hours of sun hit that area. Makes a difference.

Here is a link that might be useful: plants that love shade

I have a spot that sounds very similar, except mine gets about 2 hours of sunset light. I grew sage and basil all summer. However, I just moved them to the center of the yard now that it's October and they are much happier. I've replaced the herbs with some new types. So far peppermint seems to love the shade and Rue is looking good to. Lemon balm is not looking bad, but it's too soon to tell. I also planted lettuce. My friend is a Master Gardener and he said it will grow leggy and tall seeking out sunlight. So, I'm trying it. My mother actually grows lettuce year round. Even in the summer. She has such a dense and crazy bed that the lettuce gets shaded by all the other stuff growing around it and it grows like a monster. So, you could probably try it out in your shady spot. She grows mostly Romaine and Spinach.

my spearmint (NOT peppermint) seems to be successful through winter and summer in the shade. that seems to be a ymmv thing. peppers are also easy to grow. i have some (unknown species) that are two years old and ~like a small patio tree.