Combine 3/4 cup olive oil, the juice of 1 lemon, the paprika, dried mint, 1/2 teaspoon cumin and the red pepper flakes in a large bowl. Add the lamb and toss to coat; cover and refrigerate 1 to 4 hours.
Preheat a grill to medium high and brush the grates with vegetable oil. Thread the lamb, eggplant, artichokes and olives onto eight 10-inch skewers; season with salt. Grill the kebabs, turning occasionally, until marked, about 10 minutes for medium.
Meanwhile, make the yogurt dip: Puree the yogurt, the remaining 1 tablespoon olive oil, juice of 1/2 lemon and1 teaspoon cumin, 2 tablespoons water, the chopped mint, garlic and 1 teaspoon salt in a blender until smooth; serve with the kebabs.