Heat a large Dutch oven with a tight-fitting lid over medium-high heat. Pour in enough oil to fill the pan about 1/4-inch deep. Spread flour out on a plate or piece of waxed paper. Season half the lamb with 1 teaspoon of the salt and some pepper. Dredge in the flour and shake off the excess. Cook, uncovered, stirring only occasionally, until well browned, about 8 minutes. Using a slotted spoon, transfer the lamb to a plate. Repeat with the remaining lamb. Discard the oil and wipe out the pan.
Preheat the oven to 275 degrees F. Return the pot to the stove and melt the butter over medium-high heat. Add the onion and cook, stirring, until lightly browned, about 5 minutes. Stir in the garlic and tomato paste and cook until fragrant, about 2 minutes. Return the lamb to the pot and add the water or broth, and bring to a simmer. Using a piece of kitchen twine, tie together the parsley, thyme, and bay leaves and add the bundle to the pot. Stir in the remaining 2 teaspoons salt and pepper. Cover and transfer to the oven. Stew the meat until tender, about 1 1/2 hours.
Remove the Dutch oven from the oven. Skim the fat from the cooking liquid with a ladle. Add the potatoes, carrots, celery, and the tomatoes, and bring to a simmer. Cook the stew, uncovered, on top of the stove until the liquid has thickened and the vegetables are tender, about 1 hour. Remove and discard the herb bundle. Stir in the vinegar. Divide among bowls and serve immediately.
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