Combine lentils and chicken stock in a medium heavy soup pot.

Cover and bring to a boil.

Pulse carrot, celery, quartered onion, and garlic in a food processor until finely chopped.

Heat 1 tablespoon of canola oil in a large skillet.

Add the chopped vegetables and thyme to the skillet.

Cook over medium-high heat until softened, about 3 minutes.

Scrape the sautéed vegetables into the lentil pot.

Cover and cook over moderate heat until the lentils are tender, about 20 minutes.

Stir in spinach and season with salt and pepper.

Heat the remaining 1 tablespoon of oil in the skillet.

Add onion wedges and sausages to the skillet.

Cook over moderate heat, turning occasionally, until the onions are softened, 8 to 10 minutes.

Add balsamic vinegar and cook for 1 minute.

Thickly slice the sausages.

Stir the sausages, onions, and any accumulated juices into the lentils.

Discard the thyme sprigs.

Spoon the lentils and sausages into bowls and serve.