Combine all the chutney ingredients in a food processor or blender and pulse until well incorporated.
In a large mixing bowl, combine the ground lamb, onion, cilantro, cumin, coriander, garlic powder, and ½ teaspoon salt. Mix well, then divide the mixture into 8 small patties.
Preheat the grill to medium-high heat, and oil the grate.
Brush both sides of the eggplant slices with olive oil and season with salt and pepper.
Grill the lamb burgers for about 6-7 minutes per side until desired doneness is reached (internal temperature of 160°F for medium).
Grill the eggplant slices until just tender, about 4-5 minutes per side.
Stack each burger on an eggplant slice and top with the chutney, lettuce, tomato, and another slice of eggplant.