Melt the butter in a large saucepan over low heat. Cook the onions in the hot butter until they are golden brown, about 15 minutes.
Stir the paprika, lentils, and bulgur into the onions and coat with the butter.
Add the tomato paste, vegetable stock, and cayenne pepper; bring to a boil and cook until soft and creamy, about 1 hour.
Crumble the dried mint leaves into the soup; stir the soup and remove from heat.
Ladle into bowls and garnish with lemon slices and fresh mint to serve.