Thaw fish, if frozen. Strain juice from half of lemon into small bowl. Set aside. Thinly slice remaining lemon half. Cut the slices in halves. Set aside.
In a small mixing bowl stir together the lemon juice, oil, snipped thyme, salt, and pepper. Set aside 1/4 cup of the mixture. Toss the sliced mushrooms with the remaining mixture. Cover. Set aside.
Trim the root end plus first inch of the green tops off of the green onions; set aside.
Tuck two halved lemon slices and a thyme sprig inside the cavity of each trout. Brush green onions and the skin and inside flesh of trout with lemon juice mixture. Place fish on unheated broiler pan. (Or place in a greased grill basket.)
Broil 4 inches from the heat for 6 minutes; turn fish and place green onions on rack. Broil 4 to 6 minutes more or until fish just flakes easily with a fork, turning onions once halfway through broiling. (Or, grill fish in grill basket on the rack of an uncovered grill over medium coals for 6 minutes; turn fish and place green onions on grill rack. Grill 4 to 6 minutes more or until fish just flakes easily with a fork, turning onions once.)
Serve fish on onions. Spoon marinated mushroom slices across the top. Makes 4 servings.