Turn on the oven to preheat to 220 degrees. Put the sweet potatoes on a baking sheet, sprinkle with 2 tablespoons of oil, sprinkle with 3/4 teaspoon of salt and 1/4 teaspoon of black pepper, mix well, and put the baking sheet in a preheated oven. Fry the potatoes, stirring once, until brown, about 22-25 minutes.
Meanwhile, in a medium bowl combine fennel and onions, drizzle with lemon juice and the remaining 1 tablespoon of oil, sprinkle with 1/4 teaspoon of salt and pepper. Set the bowl aside.
Form 4 flat cutlets from minced meat, about 1.5 cm thick, sprinkle with 1/2 teaspoon of salt and 1/4 teaspoon of pepper. In a large skillet, heat 1 teaspoon of oil over medium-high heat. Place the patties in a preheated skillet and fry until tender, about 3-5 minutes on each side. At the last minute of frying, place one slice of cheese on each cutlet, and cover the pan with a lid.
Now you can fold your homemade burgers. Cut the buns into two halves. Place lettuce, cheese cutlet, and onion-fennel mixture between two halves of each bun. Serve cheeseburgers with fried sweet potatoes.