In a large skillet, heat 1/4 cup of the olive oil until shimmering. Season the trout fillets with salt and a dash of cayenne. Add the fillets to the skillet, skin side down, and cook over moderate heat for 6 minutes. Cover the skillet and cook the fillets about 6 minutes longer, until just opaque throughout. Transfer to a platter and keep warm.
Add the lettuce to the skillet and stir-fry over high heat until wilted, about 30 seconds. Season with salt and black pepper. Spoon the lettuce over the trout and keep warm.
Add the butter and the remaining 1 tablespoon of olive oil to the skillet. Add the peanuts and cook over moderately high heat, stirring constantly, until golden, about 3 minutes. Stir in the lime juice and mustard seeds, season with salt and black pepper and cook for 15 seconds. Spoon the peanuts over the fillets and serve at once.