Preheat the grill to medium-high heat.
In a large bowl, combine the shrimp, olive oil, parsley, garlic powder, salt and pepper, and lemon juice. Toss until evenly combined.
Divide the shrimp mixture into four patties and place on the preheated grill. Cook for 3-4 minutes per side, or until the shrimp is cooked through.
Meanwhile, in a small bowl, whisk together the mayonnaise, garlic, lemon juice, salt and pepper.
Toast the hamburger buns on the grill, if desired.
To assemble the burgers, divide the shrimp patties among the hamburger buns and top with the lemon-garlic aioli. Serve immediately.