Step 1Scatter onions, carrots and 4 cloves garlic across bottom of large heavy Dutch oven. Place lamb on top, skin-side up. Roast uncovered at 425 degrees 15 minutes. Turn so skin side is down and roast uncovered another 15 minutes. Remove from oven, but leave oven on.
Step 2Season lamb generously with salt and pepper, then turn and season other side (skin side should again be up). Mix 1 cup water and tomato paste and blend until smooth. Pour over lamb, along with vinegar and wine. On stove top, bring to boil, about 5 minutes.
Step 3Cover tightly and return to oven. Roast until fork penetrates very easily and meat begins to fall from bone, 5 1/2 to 6 hours. Baste lamb every hour to start, then every 1/2 hour as liquid reduces. Do not turn lamb, but occasionally push it from side to side to keep from scorching.
Step 4About 1 hour before serving, combine lentils, remaining 4 cups water, 1 teaspoon salt and remaining 2 cloves sliced garlic in large saucepan. Bring to boil, reduce heat and simmer until lentils are tender, about 45 minutes.
Step 5When lamb is done, drain lentils and add to lamb along with fresh herbs, stirring to combine cooking juices from lamb with lentils. Do not turn lamb, and stir carefully to avoid breaking up the meat. Return to oven and roast, covered, 5 minutes.
Step 6Remove from oven and adjust seasoning. Lentils should be tart, if not, add 1 to 2 tablespoons vinegar. Serve immediately.