Puncture the cotechino several times with the point of a knife so the skin won't split when it cooks. Place the cotechino in a saucepan and cover by a couple of inches with water. Bring to a boil, lower the heat, and simmer until the sausage is cooked through, about 1 hour.
In the meantime, drain the lentils and place in a pan with 1 cup water, a drizzle of olive oil, the bay leaves and onion and season lightly with salt. Bring to a boil, lower the heat, and simmer for about 45 minutes, adding a little more water if the lentils start to dry out. When the lentils are done, check the seasoning and add salt if necessary. Stir in the parsley.
Remove the sausage from the water. Slice and serve over the cooked lentils.