Preheat the oven to 425 degrees F.
Dry the lamb with paper towels and sprinkle it generously with salt and pepper. In a 5-inch-deep Dutch oven or other large ovenproof pot with a lid, heat the vegetable oil over medium-high heat until very hot but not smoking. Add the lamb in a single layer, in batches if necessary to avoid crowding, and brown well on all sides, about 15 minutes total; as the pieces are nicely browned, transfer them to a bowl.
Add the butter to the pot and melt over medium-high heat. Add the onions and cook, stirring occasionally, until translucent, 7 to 9 minutes. Add the garlic and cook, stirring, for 1 minute more.
Return the meat to the pot and add the beer. The liquid should cover the other ingredients; if it does not, add more beer.) Bring to a simmer, stirring to dissolve any brown crusty stuff in the bottom of the pan. Skim any film from the surface of the liquid, then cover, reduce the heat to low, and simmer gently until the lamb is tender, 1 1/2 to 2 hours.
While the stew is cooking, roast the vegetables: In a medium bowl, toss 1 tablespoon of the olive oil with the potatoes and salt and pepper to taste. Spread the potatoes on a baking sheet and roast, stirring frequently, until golden brown and tender, about 25 minutes. Do the same with the carrots and parsnips, tossing them with the remaining 2 tablespoons oil, spreading on one baking sheet, and roasting for about 17 minutes. Check for doneness by tasting the vegetables; they should be slightly underdone. Remove from the oven.
When the meat is tender, add the vegetables to the stew and simmer together for about 10 minutes more. Season with salt and pepper and serve.