Place lentils, water and 1 teaspoon salt in a saucepan and stir. Bring to a boil, and then reduce the heat to simmer 30 to 40 minutes, or until the lentils are tender but not falling apart. Drain in a sieve set over a bowl and reserve ½ cup of the cooking liquid.
Meanwhile in a heavy sauce pan, melt 2 tablespoon of butter over low heat. Stir in the onion, garlic, salt and cook covered until the onions are pale golden, about 10 minutes. Stir occasionally
Remove the lid and cook stirring occasionally for another 5 to 10 minutes, or until the onions are golden.
Stir the lentils into the onion along with the reserved cooking liquid and heat through. Add the lemon juice, parsley, 2 tablespoons fresh lemon juice. Pepper and olive oil. Stir gently to bind it all.
Pat dry the salmon and sprinkle with salt and pepper. In a large skillet over medium-high heat, heat 1 tablespoon butter and olive 1 tablespoon olive oil. When the butter foam subsides add the fish and cook, turning once. 5 to 8 minutes depending on the thickness of the salmon. Make sure that it is not too overcooked or it will be too dry.
When ready to eat sprinkle a couple of drops or olive oil and a small squeeze of lemon in top of the lentils. This will accentuate the flavor of the caramelized onions