Sauté onion in butter in a large skillet until tender. Stir in parsley, crayfish tails and fat, and salt and pepper; bring to a boil. Reduce heat; simmer, uncovered, 20 minutes.
If a thicker gravy is desired, dissolve cornstarch in a small amount of water, and stir into mixture. Return mixture to a boil. Reduce heat; continue to simmer, uncovered, until desired thickness is reached.
Ladle étouffée over rice in individual serving bowls. Garnish each serving with a lemon slice.
Note: 1 cup butter may be substituted for crayfish fat.