Whisk together the olive oil, lemon juice, cumin, oregano, garlic, salt and pepper in a large baking dish. Place the eggplant and onion in the dish and toss them with the marinade to coat. Let them sit at room temperature for about 15 minutes, stirring occasionally.

While the vegetables are marinating, making the tzatziki. Combine the cucumber, cashews, lemon juice, and garlic in a high-speed blender and blend until completely smooth. If the mixture is too thick, add water 1 tablespoon at a time—the sauce should have the consistency of a creamy salad dressing. Stir the dill into the sauce and season with salt to taste. Set aside.

Heat an indoor grill to high or an outdoor grill to medium. Put the eggplant and onions on the grill in a single layer (you might have to do them in 2 batches, depending on the size of your grill). Cook them for 5-7 minutes, until they're beginning to char, then flip them over and cook them on the other side until they're lightly charred and tender, about 5 minutes more.

Divide the eggplant, onions, roasted red peppers, and olives onto the pita bread and top them with tomatoes, lettuce, and tzatziki. Fold the bread over and serve.