Add 8 cups water to a large saucpan, set over high heat; when water boils, add 2 teaspoons salt and decrease heat to medium.
Whisk in cornmeal in a slow, steady stream (this should take about 1 minute); make sure to whisk the cornmeal continuously to prevent lumps from forming; continue whisking as the cornmeal comes back to a boil.
Simmer, whisking constantly, until the polenta starts to thicken, 1-2 minutes.
Decrease heat until the polenta is at the barest simmer; cover the pot and cook very slowly, stirring iwth a wooden spoon every 10 minutes or so, until the cornmeal loses its raw flavor, 35-40 minutes.
While the polenta is cooking, bring 8 cups water to a boil in a saucepan; add in the lentils, bay leaf, and garlic; simmer over medium heat until the lentils are tender but still a bit firm, about 25 minutes.
Drain; discard the bay leaf and garlic; set aside.
While the lentils are cooking, heat the oil in a saucepan, add the onion, carrot, and celery; saute over medium heat until the vegetables have softened, about 10 minutes.
Add in the tomatoes; simmer until the sauce thickens somewhat, about 10 minutes.
Add the lentils and cook for 1-2 minutes to heat through.
Stir in the parsley; season with salt and pepper to taste.
When the polenta has finished cooking, stir in the butter and add more salt if needed.
Divide the polenta among large individual bowls; spoon some of the lentils and sauce over each portion.
Serve immediately with grated cheese passed at the table.