In a large pot on medium, cook cayenne pepper, ginger, cumin and turmeric until fragrant. This toasts the spices to draw out the flavors.
Add coconut oil, onion and garlic and stir to mix with spices and cook until softened.
Stir in grated apple and red lentils.
Stir in coconut milk and water.
Bring spicy coconut milk mixture to a boil.
Reduce temperature to simmer and cook until lentils are soft, about 30 minutes.
Add lime juice, salt and pepper. Season additionally with salt to taste.
Serve with a generous spoonful of plain yogurt and cilantro leaves for a nice tang.