Melt the butter in a large Dutch oven over medium-high heat. Add the onion, season with salt and pepper and cook, stirring, until the onion is translucent, about 5 minutes.
Add half the chopped apples, and cook, stirring until softened, adjusting the heat as necessary to avoid burning, about 5 minutes.
Add the celery, garlic and thyme, and stir to combine. Pour in the cider and wine and let it come to a boil. Add the sausage, lentils, nutmeg and water to the pot. Season with 1 tsp salt and 1 tsp freshly ground pepper. Let the soup come to a boil, then decrease the heat to maintain a low simmer.
Cover the pot and cook until the lentils are tender, 40 to 50 minutes.
Before serving, add the vinegar. Stir together the Greek yogurt and the mustard, then stir the mixture into the soup. Taste and add more salt and pepper if needed. Serve in bowls topped with the green onions, fresh arugula, and remaining chopped apples.