Preheat the oven to 350℉ (176℃).
To make the crust: Blend the flour, softened butter, and sugar in a medium bowl until well combined; press into the bottom of an ungreased baking dish, about 1/2 inch thick.
Bake in the preheated oven until firm and golden, about 15 minutes. Meanwhile, make the filling: Whisk the sugar and flour in a medium bowl. Whisk in eggs, then lemon juice until smooth; pour filling over the baked crust.
Bake for 20 minutes. Set the pan aside to cool completely; the bars will firm up as they cool. When cooled, cut into uniform squares. Dust with powdered sugar before serving.
Heat a pot over medium heat. Once hot, add the oil. Sauté the sausage until nicely browned, then add the onion, carrot, celery, and garlic until softened. Season with salt and pepper.
Stir in the broth, thyme, and lentils. Bring to a simmer until the lentils are soft and the soup builds flavor. (If the soup is too thick, thin it out with a little more broth.) Remove the thyme sprigs. Season with salt and pepper to taste.
Toast the bread.
Serve the stew with bread and sparkling water. Garnish with parsley. Enjoy with lemon bars.