Preheat oven to 325° F. with oven rack in lower middle position.
Season the meat with salt and pepper.
Evenly divide 5 Tbsp of the oil into as many batches as needed to brown meat and bones without overcrowding. Heat the oil in a large Dutch oven over medium-high heat then add meat and bones, not moving anything until it is well browned and doesn't stick to the pan, about 2-3 minutes. Turn the pieces with tongs and cook until brown on all sides. Remove the browned meat and bones to a large bowl, heat up more oil, brown the meat and bones as before and repeat this process until all the meat and bones are browned and in the bowl.
In the same Dutch oven, heat 2 Tbsp of oil over medium heat. When the oil is hot, add the carrots and turnips, season with salt and pepper, and brown on all sides. Remove the vegetables from the Dutch oven and put together in a separate bowl.
Again in the same Dutch oven, heat the remaining 2 Tbsp oil over medium heat. Add the onions and cook until softened, about 5 minutes, stirring frequently and scraping the bottom of the pot to loosen whatever starts to stick. Add the flour and cook another 2 minutes or so, stirring frequently to evenly coat the onions with the flour.
Stir in 3 cups of the water, stirring and scraping the bottom and sides with a wooden spoon to loosen any brown bits along the bottom and sides of the Dutch oven. While stirring continuously, add the remaining 3 cups of water until the flour is dissolved. Bring to a simmer, add the thyme, some salt and all of the meat, bones and accumulated juices. Bring back to a simmer, cover the pot, and cook in the oven for 45 minutes.
After 45 minutes, stir in the carrots and turnips, return the covered pot to the oven and cook another 45 to 75 minutes, or until the lamb is tender.
If you are serving this stew right away, let it sit a few minutes so you can spoon the fat off of the top. You can then serve as is or, if you prefer, put on heat-proof gloves and separate meat from bones (easy to do as the meat falls off the bones at this point) , discarding the bones or serving them separately. Either way, add the parsley and chives and check for seasoning right before serving
If you are serving the stew later--up to 3 days later--let it cool then if you want, separate the meat from the bones as above. Cover the pot, put the bones in a separate container (if separating) and refrigerate. When ready to reheat, remove the hardened fat from the top of the Dutch oven and reheat in oven at 325 ° F. or on top of the stove. Reheat the bones separately. Add the parsley and chives to the stew and check for seasoning right before serving.