Preheat oven to 425°F. Place naan breads on a baking sheet (you may need two sheets).
Build the base. Brush each naan with olive oil all the way to the edges. Scatter the pizza cheese blend evenly over all four, then top with the chopped sun-dried tomatoes.
Bake for 8–10 minutes, until the cheese is bubbling and the naan edges are golden and crisp.
Top and finish. Remove from the oven. Fan sliced avocado over each pizza. Scatter fresh basil over everything. Zest both lemons generously over the top, then squeeze the juice over as well. Drizzle with finishing olive oil and season with flaky salt and black pepper.
Serve immediately. Slice and eat right away — the contrast of warm crispy naan and cheese against cool avocado is the whole point.