Finely shred lemon peel from lemon and juice lemon to get 2 tablespoons. In a large bowl stir together lemon juice, mayonnaise, and the 1 tablespoon water. Use a fork to mash one of the hard-cooked egg yolks into mayonnaise mixture. Season to taste with salt and pepper.
Coarsely chop remaining hard-cooked eggs. Add to mayonnaise mixture along with avocado and onion; stir to coat.
To serve, spoon egg mixture over tomato slices. Top with walnuts and desired amount of lemon peel. If desired, season with additional salt and pepper.