Bring 4 cups water to a boil. Add the lentils and 1 teaspoon salt and simmer, stirring occasionally, until tender, 20 to 25 minutes. Drain.
Meanwhile, heat 1 teaspoon of the oil in a large nonstick skillet over medium-high heat.
Season the salmon with ¼ teaspoon each salt and pepper and cook until opaque throughout, 4 to 5 minutes per side.
In a large bowl, combine the vinegar, mustard, onion, parsley, remaining 2 tablespoons of oil, and ¼ teaspoon each salt and pepper.
Add the lentils and arugula to the vinaigrette and toss to combine. Serve with the salmon and lemon wedges.