Cook french fries according to packaging. While fries are in the oven, form four patties from the ground lamb (1/2 pound each). Season liberally each side with salt and pepper. Heat a cast iron skillet on medium-high heat. Add butter to skillet. Cook burgers on each side for about 4 minutes for medium rare.
While burgers are cooking, mix the harissa paste into the goat cheese. Season with salt and pepper to taste.
When fries are finished, place them in a large mixing bowl and season with salt, pepper, and about 3 parts paprika and 1 part chili powder, to taste. Mix the seasoning around so that it evenly covers all the fries. You can use a wooden spoon or just toss the bowl using both hands, flipping the fries slightly with each toss.
Let burgers rest for 1-2 minutes before serving. Place on the bun and then top with goat cheese and bibb lettuce