Combine the mashed avocado with the lemon juice, salt, and pepper. Spread evenly over the pieces of toasted bread.
Spray a medium skillet with nonstick spray or butter. Over medium heat, cook the eggs sunny-side up for about 3 minutes (or until the egg white is cooked but the yolk is runny).
Place the sunny-side-up eggs on the mashed avocado toasts. Drizzle with labneh and garnish with POM Arils, za’atar, and fresh dill. Serve immediately.