For the harissa aioli:   

In a small bowl whisk together the mayonnaise, harissa and garlic until combined then cover with plastic wrap and refrigerate until ready to use. Can be made up to a week in advance and stored, refrigerated. 

For the lamb burgers:  

Divide the ground lamb into 4 equal portions and flatten into patties. Lay out on a parchment paper-lined baking sheet and season on both sides with the salt, pepper and garlic powder. 

Heat a large cast iron skillet over medium-high heat then add 1 tablespoon of the olive oil and heat through. Add two of the patties to the pan and cook until the burgers are golden brown and slightly charred, about 3 minutes. Flip the burgers and cook for an additional 4 minutes for medium-rare. Repeat with the remaining oil and burger patties.

For assembly: 

Preheat oven to broil. Arrange the hamburger buns cut sides up on a baking sheet and broil until golden brown, about 1 to 2 minutes. Spread the bottom half of the bun with the goat cheese then top each with a lamb burger and top with a slice of tomato and a handful of Arugula. Spread a tablespoon of the aioli on the top half of the bun and close. Repeat with the remaining burgers. Serve immediately.