Preheat oven to 350ºF. Cut any overly large chunks of lamb into bite-sized pieces and season lamb generously with salt and pepper. Heat oil in a heavy Dutch oven over medium flame. Working in batches, brown the lamb (you may need to drizzle in a little more oil between batches). During the last batch, reduce heat slightly. Transfer lamb to bowl and set aside.
Add onion to pot and cook, stirring frequently, until translucent, about 3 minutes. Don't let it brown. Add garlic and tomato paste and sprinkle in 2 tablespoons of flour. Cook, stirring frequently, until tomato paste and flour are slightly browned, about 2 minutes. Add water and wine to pot and scrape up browned bits. Add thyme and bay leaf and return lamb to pot, along with any accumulated juices. Increase heat and bring to a boil. Cover Dutch oven and transfer to oven. Braise for about 30 to 40 minutes.
Meanwhile, melt 2 tablespoons of butter in a medium skillet over medium heat. Add turnips, carrots and shallots and sprinkle with sugar. Toss to coat and cook, stirring occasionally, until vegetables have softened and browned slightly, about 10 minutes.
Add browned vegetables (don't fret if they don't brown) and potatoes to Dutch oven and return to oven. Braise until vegetables are tender, 30 to 40 minutes. Transfer Dutch oven to stovetop.
Wipe vegetable skillet clean and melt remaining 2 tablespoons of butter over medium heat. Add remaining 2 tablespoons of flour and cook, whisking constantly, until the mixture is nicely browned and the flour has lost its raw taste, about 5 minutes. (You're making a blond roux to thicken the stew's liquid—see Kitchen Notes for other options.) Add roux and peas to Dutch oven, bring to a boil and reduce to a simmer. Cook for 5 minutes or so, until peas are just cooked. Ladle stew into shallow bowls and serve. Some crusty bread makes a good accompaniment.