To prepare pickled onion, combine onion and vinegar in a bowl. Let stand 30 minutes; drain.
To prepare dressing, combine oil and next 8 ingredients (oil through minced garlic), stirring with a whisk.
To prepare salad, leave root and 1 inch stem on beets; scrub with a brush. Place in a medium saucepan; cover with water. Bring to a boil; cover, reduce heat, and simmer 20 minutes or until tender. Drain and rinse with cold water. Drain; cool. Trim off beet roots; rub off skins. Cut beets into 1/2-inch cubes; place in a large bowl. Set aside. Place lentils, carrot, 2 garlic cloves, and bay leaf in a large saucepan; cover with water to 2 inches above lentils. Bring to a boil; cover, reduce heat, and simmer 20 minutes or until tender. Drain well. Discard garlic cloves and bay leaf. Add lentil mixture, pickled onion, dressing, 1/3 cup parsley, capers, 1/8 teaspoon salt, and 1/8 teaspoon pepper to beets. Set aside.
To prepare slaw, toss cabbage with red wine vinegar and 1/8 teaspoon salt. Divide slaw evenly among 4 plates; top with salad. Garnish with chopped parsley, if desired.