Pulse nuts in a food processor with 1/4 cup of flour until finely ground. Rinse trout and pat dry. Season with salt inside and out.
Put the remaining 2 cups flour in a pie plate. Beat the egg in a pie plate. Spread ground nuts on a dinner plate. Dip both sides of trout first in flour (pat off the excess), then egg, and then nuts. Heat oil in a 12-inch heavy skillet over moderate heat until hot but not smoking and cook trout, shaking skillet to prevent sticking and turning once with a metal spatula, until browned on both sides and just cooked through, about 12 minutes total.
While trout is cooking, melt butter in a small saucepan and stir in lemon juice. Season with salt and pepper and keep warm. Pour over trout and sprinkle fish with parsley.