In a clean skillet melt 2 tablespoons of butter on medium heat. Next, add the Brussel sprouts and season with a pinch of salt and pepper.
Sauté the Brussel sprouts until they are tender, about 5 minutes, mixing occasionally. Remove Brussel sprouts from skillet and set aside.
Return the skillet to high heat and melt 2 tbsp. of butter. Next, add the salmon and sear on both sides until golden brown, about 3 minutes a side, for a total of about 6 minutes.
Next, add the lemon juice and sauté for an additional 1 minute while spooning the liquid from the skillet over the salmon.