In a bowl, mix all ingredients. Season with pepper.
Set aside in the refrigerator.
Zucchinis:
In a cast iron skillet (or non-stick skillet) over medium-high heat, soften the zucchinis in olive oil with garlic until golden brown. Season with salt.
Add lemon vinegar, let reduce for 1 minute, then remove from heat.
Lamb Patties:
Preheat the barbecue to high heat. Oil the grill.
In a bowl, mix all the ingredients. Shape into 4 patties using your hands.
Grill the patties on the barbecue for 4 to 5 minutes on each side. Toast the buns.
Spread the inside of the buns with yogurt sauce, then add lettuce leaves. Place the patties on top and distribute the zucchinis. Garnish with mint leaves and close the burgers.