Bring lentils, water and 1/2 teaspoon salt to a boil in a 2-quart heavy saucepan, then reduce heat and simmer, uncovered, until lentils are just tender but not falling apart, 12 to 25 minutes.
While lentils simmer, cut fennel bulb into 1/4-inch dice and chop enough fennel fronds to measure 2 tablespoons. Heat 3 tablespoons olive oil in a 3 to 4 quart heavy saucepan over moderate heat until hot but not smoking, then stir in onion, carrot, fennel bulb, fennel seeds and remaining teaspoon salt.
Cover pan and cook, stirring occasionally, until vegetables are very tender, about 10 minutes.
Meanwhile, lightly prick sausages in a couple of places with tip of a sharp knife, then cook sausages in remaining 1/2 tablespoon olive oil in a 10-inch nonstick skillet over moderately high heat, turning occasionally, until golden brown and cooked through, 12 to 15 minutes.
Transfer to a cutting board.
Drain cooked lentils in a sieve set over a bowl and reserve cooking water. Stir lentils into vegetables with enough cooking water to moisten (1/4 to 1/2 cup) and cook over moderate heat until heated through.
Stir in parsley, pepper, 1 tablespoon vinegar and 1 tablespoon fennel fronds. Season with vinegar and salt.
Cut sausages diagonally into 1/2-inch thick slices. Serve lentils topped with sausage and sprinkled with remaining tablespoon fennel fronds.