Whisk the lemon juice, 1/2 t salt, and 1/4 t pepper in a medium bowl. Gradually whisk in the oil to blend. Set the dressing aside.
Cut the regular tomatoes into 1/2-inch thick slices, and the plum tomatoes into wedges. Cut the cherry, grape, and teardrop tomatoes in half. Arrange the tomatoes and mozzarella on a platter. Drizzle the dressing over. Sprinkle with the basil and additional salt and pepper to taste, and serve.