In a medium saucepan, cover the lentils with 2 inches of water and bring to a boil. Add 1/2 teaspoon of salt. Simmer the lentils over low heat, stirring occasionally, until tender, about 25 minutes. Drain and transfer to a bowl.
Heat the olive oil in the saucepan. Add the shallot and cook over moderate heat until softened, about 3 minutes. Stir in the lentils and remove from the heat. Add the vinegar and season with salt and pepper. Stir in the radishes and parsley, transfer to bowls and serve.