Heat olive oil in a large skillet over medium-high heat. Add onion, garlic, salt, pepper, and vegetarian burger; cook 5 minutes or until vegetables are tender, stirring occasionally to crumble up the vegetarian burger.
Add lentils, cumin, and thyme; stir until seasonings become fragrant. Add 1/2 cup water, tomatoes, and bay leaf; bring to a boil. Cover, reduce heat to medium, and cook 15 minutes or until lentils are tender and mixture is thick (add additional water as needed). Discard bay leaf.
Fill each pita half with 1/2 cup lentil mixture. Spoon 1 Tbsp yogurt into each pita half; top with 2 Tbsp cucumber. Sprinkle with mint if desired.