In medium saucepan, combine lentils with water. Bring to boil then reduce heat to simmer; cover and cook 15 minutes. Turn off heat and allow lentils to steam 5 minutes; drain and let cool.
In medium bowl, combine lentils, shallot, grapes, dill, walnuts, lemon juice, lemon zest, vinegar, 1 tablespoon olive oil, arugula, 1/4 teaspoon salt, and pepper, to taste; set aside. Heat oven to broil. Move rack to highest position.
Sprinkle trout fillets with lemon zest, remaining salt, and 1/4 teaspoon pepper; brush with remaining olive oil. Broil trout 4-5 minutes. Serve with lentil salad.