The pizza toppings -- avocado, tomatoes, and sour cream -- don't require any cooking.
Toss onion, tomatoes, and avocados with oil and lime juice in a medium bowl. Season with salt and pepper; set aside.
Heat a grill until medium-hot. Generously brush one side of pizza dough with oil; grill, oiled side down, until underside is golden brown and top begins to bubble, 3 to 5 minutes. Quickly brush top with oil; flip crust. Top with a layer of cheese. Grill until melted and crust is cooked through, 3 to 5 minutes more.
Slide pizza with a large spatula onto a cutting board. Season with salt and pepper. Top with avocado mixture. Dot with sour cream and serve with limes, if desired. Repeat to make more pizzas.