In a food processor, combine the parsley and garlic with 2 Tbsp. of water and whir until the mixture is completely smooth.
Thin the mixture with an additional 2 Tbsp. of water and mix well.
Add the lemon juice and salt and pepper to taste. Set aside, covered.
On a flat plate combine the flour with about 1/2 tsp. each of salt and pepper and mix well.
Into this dip the fillets, coating well and shaking off whatever excess adheres.
In a large, heavy skillet heat the oil and in this fry the fillets until well browned on both sides.
Transfer the fish to a preheated serving platter and set aside to keep warm.
Discard about half of the oil and in the remaining oil saute the onions until golden brown.
Add the remaining flour and over a low flame cook until the mixture is light brown, stirring constantly.
Add the parsley mixture and cook, continuing to stir, for 2 – 3 minutes longer.
Pour the sauce over the fillets and serve immediately.