Preheat the grill to medium-high heat.
In a bowl, combine the ground lamb, breadcrumbs, red onion, garlic, mint, oregano, salt, and pepper. Mix the ingredients until well combined. Divide the mixture into 4 equal portions and shape them into burger patties.
Brush the grill grates with oil to prevent sticking. Place the lamb burger patties on the grill and cook for about 4-5 minutes on each side, or until they reach your preferred level of doneness.
While the burgers are grilling, prepare the spring slaw. In a large bowl, combine the sliced asparagus, red onion, and sugar snap peas. Add the chopped mint and parsley.
In a small resealable container, mix the olive oil, lemon juice, salt and pepper to taste. Shake vigorously to combine. Pour over the salad and toss to coat.
Lightly brush the burger buns with olive oil and place them on the grill to toast for a minute or two.
Mix the mayonnaise and Dijon together in a bowl.
Assemble the grilled lamb burgers by spreading the mayo mixture on the top bun, then placing the cooked patties on the toasted buns and topping each with a generous portion of the spring slaw.