Melt 1 tablespoon butter in a medium saute pan; add bread cubes. Cook over medium heat until golden, stirring frequently, about 2 minutes. Drain in a paper-towel-lined bowl; set aside.
Cut ends off lemons, and remove peel, pith, and outer membranes, following the curve of the fruit with a paring knife. Lift sections away from membranes, and reserve. Squeeze juice from membranes over sections before discarding.
Melt remaining tablespoon butter and olive oil in a large saute pan over medium heat. Season trout fillets with salt and pepper, and place in pan. Saute until golden brown, about 2 minutes on each side. Remove from heat; transfer fillets from pan, and keep on a warm plate. Add lemon sections and juice, capers, and parsley to warm pan, and toss to combine. Serve fish topped with sauce and reserved croutons.