Wash the lentils using a sieve. Boil them inplenty of water for 5 minutes, drain and wash again. Put them back into the pot together with 4 cups of water and boil in medium heat for 15-20 minutes.
In a nonstick pan, add the olive oil and sautee the onions and garlic until they turn clear. Then add the rice and stir for 1-2 minutes. Take the pan away from the heat and add the onion, garlic and rice mixture to the pot with the lentils.
Add the salt and pepper, tomato puree, bay leaves, a little bit of warm water, if needed, and cook at medium heat for about 20 minutes, until most of the liquid is gone. Serve with vinegar.