Clean and cut the mushrooms into ¼ inch dice, and sprinkle them with lemon juice.
Melt 1 ounce of the butter in a small saucepan and soften the onion for several minutes without letting it brown.
Stir in the mushrooms and let them stew gently for 5 minutes, covered.
Season with salt and stir in the chopped parsley; keep the mixture hot.
Break the eggs into a bowl and season with a little salt.
Beat briefly with a fork until well mixed but do not over-beat as this will make the omelet tough.
Heat half of the remaining butter in an omelet pan.
At the moment when it starts to brown, pour in half the eggs, let them fry, moving them around briskly with a fork for a minute and lifting the edges to allow the uncooked mixture to run underneath.
When just set put half the mushrooms across the middle and slide the omelet onto a heated plate, folding it over to make a half-moon shape as you do so.
Fry the second omelet in the same way.