Beat together eggs, milk and seasonings with a fork. Heat a 10-inch (25 cm) non-stick skillet over medium-high heat. Add butter. When melted, pour in egg mixture. As eggs begin to set at the edges, use a spatula to gently push cooked portions to the centre, tilting the skillet to allow the uncooked egg to flow into empty spaces.
When egg is almost set on surface but still looks moist, spoon salsa on top and garnish with avocado slices sprinkled with lemon juice. Top with cheese. Place skillet under broiler just until cheese is melted, about 30 seconds.
Cut omelet into wedges and serve.