Pick over and rinse the lentils, and put them in a 3- to 4-wuart saucepan. Pile the thyme, bay leaves, garlic, and peppercorns on a 5-inch square of double-layer cheesecloth. Gather up the edges and tie into a little pouch with kitchen twine. Add the pouch to the pan along with the onion and carrot. Fill the pan with cold water to cover the lentils by about 2 inches, and bring to a boil over medium-high heat. Immediately lower to a gentle simmer-boiling can break the lentils-and simmer, uncovered, until just tender, 30 to 40 minutes. (If the water level drops below the surface of the lentils as they simmer, add a little more water.)

Meanwhile, put the sausage in a small saucepan or deep skillet. Add the wine and enough water to cover by about 1/2 inch. Bring to a simmer. Reduce the heat as needed to cook at a bare simmer (bubbles should only occasionally break the surface), uncovered, until a metal skewer inserted into the center comes out feeling hot to the touch, 15 to 20 minutes.

While the lentils and sausage cook, make the vinaigrette: In a medium bowl, whisk 1-1/2 tablespoons of the vinegar with the mustard and a pinch of salt. In a steady stream, whisk in the olive and walnut oils. Season to taste with salt.

Drain the lentils, discarding the herb pouch, carrot, and onion. Transfer to a large bowl and add 1 teaspoon salt and the remaining 1 tablespoon vinegar, tossing to coat.

Drain the sausage, and, if necessary, peel off the casing (bite into a piece first--many sausage casings are thin enough to leave on). Slice into 1/4-inch rounds. Add the sausage and vinaigrette to the lentils, tossing to coat. Stir in the parsley and scallions, and season with a generous amount of black pepper, plus more salt and vinegar to taste.