Set the Anova Sous Vide Precision Cooker to 143ºF.
Put the lamb shanks into two bags with four sprigs of thyme per bag. Seal the bags using the water immersion technique or a vacuum sealer on the moist setting.
Place the bags in the water bath and set the timer for 48 hours. Cover the water bath with plastic wrap to minimize water evaporation. Add water to the water bath, as needed, to keep the shanks submerged.
About 45 minutes before the lamb is finished, heat the oven to 410ºF.
Place the sweet potatoes on a small baking sheet and transfer to the oven. Bake until soft, about 40 minutes.
Meanwhile, prepare the salad: Combine the apple, fennel, and walnuts in a medium bowl. Toss with 4 tablespoons olive oil, lemon juice, and capers. Season to taste with salt and pepper.
When the sweet potatoes are soft, remove from the oven. Peel off the skin and discard. Transfer sweet potato flesh to a medium bowl. Add the remaining tablespoon olive oil and, using a fork, mash until smooth. Season to taste with salt and pepper.
When the timer goes off, remove the bags from the water bath. Remove the shanks from the bags and pat very dry with paper towels.
Melt the butter in a large skillet over medium-high heat. When the butter stops foaming, add the shanks. Sear shanks until well-browned on all sides, 3 to 5 minutes total. Transfer to a platter and keep warm.
Return the skillet to medium-high heat and add the red wine. Bring to a rapid simmer and reduce, stirring occasionally, until thickened into a sauce, about 5 minutes.
Divide the mashed sweet potatoes between two serving plates. Top each serving with a lamb shank. Drizzle with the red wine reduction. Serve the salad on the side.