Preheat the oven to 425 degrees F. Meanwhile, heat the oil until hot in a grill pan or skillet over medium-high heat, then add the chicken. Cook thoroughly, about 5 minutes on each side, then remove from the pan.
Add more oil to the pan as necessary, and add the mushrooms, peppers, onions, fajita seasoning and 1/2 teaspoon each salt and pepper and cook until the vegetables are slightly tender, tossing with tongs periodically, about 5 minutes. Remove from the pan.
Place the naan on a baking sheet, pizza pan or baking stone. Top each piece with a layer of tomato sauce, followed by the chicken, vegetables and then the cheese. Bake until the cheese has melted, 10 to 15 minutes. Top the pizzas with the avocado, cilantro and freshly squeezed lime juice, if using, then divide each pizza in half and serve.
If you don't have fajita seasoning on hand, use 1/2 teaspoon each of ground cumin and chili powder.