In a bowl, toss onion with lemon juice and sprinkle with salt and pepper. Set aside.
In a shallow pan, beat eggs with water.
Heat 1 tablespoon oil in a large skillet over medium heat.
Dip each fillet in the egg, then add to the hot skillet, working in batches. Cook for about 5 minutes, flipping once, then drain on paper towels. Repeat for remaining fillets with the second tablespoon of oil.
Squeeze a lemon wedge over each serving, then top with pickled onions.