Whisk together the olive oil, lemon juice, cumin, oregano, garlic, salt and pepper in a large baking dish. Place the vegetables in the dish and toss them with the marinade to coat. Let them sit at room temperature for about 15 minutes, stirring occasionally.
Heat an indoor grill to high or sear. Put the veggies 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 just 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 veggies onto the pita bread and top them with tomatoes, lettuce, and Creamy Cucumber Dill Sauce. Fold the bread over and wrap the bottom half tightly with foil.
If you don't have an indoor grill, you can use a grill pan or an outdoor grill for the veggies. If you're using an outdoor grill, use a basket so the veggies don't fall through the grates!