Bring a large pot of well-salted water to a boil over high heat.
Meanwhile, heat the olive oil in a 12-inch skillet over medium-high heat. Add the fennel, onion, and 1/2 tsp. salt. Cook, stirring frequently with a wooden spatula, until softened and just starting to brown, about 4 minutes.
Add the lamb, 1/2 tsp. pepper, and another 1/2 tsp. salt and cook, stirring to break up the meat, until lightly browned and cooked through, about 4 minutes.
Move the mixture to the side of the pan and carefully tilt the pan to pool any fat on the empty side. If necessary, spoon off all but about 2 Tbs.
Add the tomato paste and mash it on the bottom of the skillet to brown it slightly, about 1 minute, before stirring it into the meat. Add the wine and cook, stirring and scraping the bottom of the skillet to loosen any browned bits, until most of the liquid has evaporated, about 2 minutes.
Add the tomato juice and continue to cook, stirring occasionally, until the sauce thickens and clings to the meat, about 2 minutes. Season to taste with salt and pepper. Add the fennel fronds and oregano, cook for 1 minute longer, and remove from the heat.
Cook the tagliatelle in the boiling water until just al dente, 3 to 4 minutes. Reserve 3/4 cup of the water and then drain the pasta.
Return the skillet to medium-low heat, add the drained pasta to the sauce and stir to blend. Loosen with a little of the pasta cooking water if necessary and serve topped with grated cheese.