For the sea trout, season the sea trout fillets all over with salt and freshly ground black pepper.
Heat the oil in a large frying pan over a medium heat. Add the trout fillets, skin-side down, and fry without moving the fish for 4-5 minutes, or until the skin is crisp and golden-brown.
Turn off the heat, then turn over the trout fillets and allow the undersides of the fillets to cook through on the residual heat.
Meanwhile, for the peas and horseradish, blanch the peas and carrot batons in a pan of boiling salted water for 1-2 minutes, or until just tender. Drain well, refresh in cold water, then drain again.
Blanch the bacon lardons for one minute in a separate pan of boiling water, then drain well.
Heat one tablespoon of the butter cubes in a large saucepan over a high heat. When the butter is foaming, add the blanched bacon lardons and fry until crisp and golden-brown.
Add the blanched carrots and peas to the pan with the bacon lardons in it. Pour over the chicken stock and bring the mixture to the boil, then reduce the heat to a simmer and simmer the mixture for 4-5 minutes. Season, to taste, with salt and freshly ground black pepper.
Add the butter cubes, a few at a time, to the mixture, shaking the pan regularly until the butter melts and the sauce has thickened slightly before adding the next few cubes.
Add the shredded Little Gem lettuce leaves and horseradish cream and stir well, then remove the pan from the heat.
To serve, divide the vegetables and sauce equally among four serving bowls. Place one trout fillet on top of each serving. Serve immediately.