For the caramelized onions: Cook the onions in the butter and oil in a skillet over medium-low heat, stirring occasionally, until caramelized, about 20 minutes. Set aside.
For the pizza: Cook the sausage in a skillet, breaking up with a wooden spoon, until crumbled and cooked through. Set aside.
Adjust an oven rack in the middle position and preheat the broiler to high. Add the oil to a large nonstick skillet over medium heat, then add a tortilla; this will start crisping the bottom of the tortilla before it goes in the oven. Almost immediately, build the pizza right in the pan, starting with a quarter of the tomatoes followed by the a quarter of the cheese, making sure the cheese goes all the way to the edge and beyond. Then add a quarter of the onions and a quarter of the sausage. Transfer the skillet to the broiler and cook until the cheese is golden brown and melted, 4 to 5 minutes. Repeat with the remaining pizza ingredients to make 3 more pizzas. (You can hold the pizzas in a warm oven while you make the others.)
For the salad: Place the lettuce in a salad bowl. Top with the tomatoes and bacon and drizzle with dressing.