In a small bowl, mix the yogurt with the mint, garlic and 1 tablespoon of the lemon juice. Season the yogurt sauce with salt and pepper and refrigerate.
In a mini food processor, combine the dried currants, pine nuts, chopped parsley, lemon zest, cumin, coriander and cinnamon with the remaining 1 teaspoon of lemon juice and 1 teaspoon of salt. Process the ingredients until a coarse paste forms.
Scrape the currant–pine nut paste into a large bowl and add the ground lamb. Using your hands, gently mix the ground meat thoroughly with the seasonings and pat into 4 plump burgers. Set the burgers on a plate, cover them with plastic wrap and refrigerate for 15 minutes.
Light a grill. Lightly brush the grate with oil. Grill the burgers over a medium-hot fire for 6 minutes per side for medium rare. Grill the buns, cut side down, until toasted. Set the burgers on the buns and serve with the mint-yogurt sauce.
The yogurt sauce and burger patties can be refrigerated overnight. Let the burgers stand at room temperature for 15 minutes before grilling.