1. Ask your butcher to cut the liver for you, separating the 'dark' from the 'white' parts. Peel the onions, cut them in half, then slice them. Pour the olive oil into a pot, and once it's hot, add the onions and sauté them for about 25-30 minutes until they caramelize.
2. Stir occasionally. Remove the onions from the pot and place them in a colander. Return any oil that drains from them back into the pot. Add the 'white' liver to the pot, which you have rinsed well (don't drain it completely, and add a little more water – this will help it cook) and fry for 10 minutes.
3. Then add the 'dark' liver, which you also rinse and drain slightly, and continue frying for 10 minutes. Stir occasionally. Return the onions to the pot and mix.
4. Simmer the dish over low heat for 15 minutes to allow the flavors to meld. Stir occasionally.
5. Before removing the dish from the heat, add the salt (at the end so the liver doesn't toughen), pepper, and lemon juice. Stir and let the liver finish cooking.