Clean the lentils with fresh cold water to avoid foaming when cooking.
Mix 2 cups of lentils with the 8 cups of water and 1 tablespoon of salt.
Heat on high, uncovered for approximately 30 minutes, mixing slightly every 10 minutes, removing any foam that may have come up.
After the lentils turn tender and soft (not melted), make sure there is only about 2 cups of water remaining (add or remove water).
Add the half cup of rice. Cook for 10 mins at medium fire.
Simultaneously with the rice, fry the chopped cup of onion in the olive oil and vegetable oil until golden brown (should be about 10 minutes).
After the 10 minutes pass, slowly pour the oil and onion over the lentils and rice. Lower the heat to Low, and let it lay for 10 minutes (do NOT mix).
After the 10 minutes pass, add the quarter cup of vinegar and mix everything.
Cover with a thick clean kitchen towel and leave covered for about 10 minutes.
After the 15 minutes pass, you should have a thick pilaf of lentils and rice, with onions showing up here and there.