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 saucepan, melt 2 tablespoons 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 and parsley, then stir in the reserved cooking liquid. 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 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 of olive oil and a small squeeze of lemon on top of the lentils. This will accentuate the flavor of the caramelized onions
Notes
I am partial to green du Puy Lentils. For me, they cook best because they are not too starchy. Make sure, however, that the lentils are rinsed well and picked over carefully.
Giangi's Kitchen provides nutritional information, but these figures should be considered estimates, as a registered dietician does not calculate them.