Stew the lentils: Place lentils, shallot, garlic, bay leaf, and enough water to cover ingredients by 2 inches (about 5 cups) in a medium saucepan and bring to a boil. Reduce heat and simmer until lentils are tender, about 20 minutes. Drain liquid and return lentils to pan. Season with salt and pepper. Stir in vinegar and 2 tsp oil.
Toast pita over the flame of a gas burner, turning with tongs, until crisp and golden brown. (You can also char in the broiler.) Brush pita with remaining oil. Stuff pita with 1/4 cup lentils, tomatoes, yogurt, and mint.