In a large bowl, whisk together 2 tbsp. olive oil, soy sauce, Worcestershire, red wine, 1 tsp. salt, and 1/2 tsp. pepper. Stir in lamb and refrigerate 3 hours or overnight.
Prepare a gas or charcoal grill for indirect heat. If using a gas grill: Turn all burners to high and close lid. When temperature inside grill reaches 400°, lift lid and turn off one of the burners. The area over the turned-off burner is the indirect heat area. If using a charcoal grill: Light 50 to 60 briquets and let burn until covered with ash, 20 to 30 minutes. Mound to one side. The area over the section cleared of coals is the indirect heat area.
In a large bowl, toss peppers, onions, eggplant, zucchini, and tomatoes with remaining olive oil, remaining salt and pepper, and garlic. Transfer vegetables to a rimmed baking sheet (not nonstick).
Put baking sheet on indirect heat area and cook until vegetables are beginning to get very tender, 30 to 60 minutes, tossing vegetables every 15 minutes. Drizzle vegetables with balsamic vinegar, toss to coat, and cook 15 minutes more. Remove baking sheet from grill and let vegetables cool.
Prepare grill for lamb: If using gas, turn all burners to medium-high. If using charcoal, add about 5 briquets (if the coals look significantly burned down) to bring the heat back to medium-high.
Toast walnuts in a medium frying pan over low heat on the stovetop, tossing frequently, until light golden and fragrant, about 10 minutes. Transfer to a medium bowl and toss with feta and cooled vegetables.
Skewer lamb onto 4 metal skewers (10 to 12 in.) and grill 5 minutes per side for medium (if using charcoal, grill over direct heat). With a fork, push lamb off skewers and into a bowl.
Spoon vegetable mixture into halved pita and top with lamb if you like.
Note: Nutritional analysis is per mini sandwich.