In a small bowl stir together the tomato, the onion, the jalapeno, the coriander, the lime juice, and salt and pepper to taste until the salsa is combined well.
In a bowl whisk together the eggs, the water, and salt and pepper to taste.
In an 8-inch skillet, preferably non-stick, heat 1/2 tablespoon of the butter over moderately high heat until the foam subsides, pour in half the egg mixture, tilting the skillet to spread the mixture evenly over the bottom, and cook it for 1 minute, or until it is almost set.
Sprinkle half the omelet with half the bacon, half the avocado, peeled and cut into 1/2-inch pieces, and half the Monterey Jack and cook the omelet for 1 minute, or until it is set.
Fold the omelet over the filling, transfer it to a plate, and keep it warm.
Make another omelet in the same manner with the remaining butter, egg mixture, bacon, avocado, and Monterey Jack and serve the omelets with the salsa.