Place lamb, zucchini, and summer squash in a large shallow baking dish or resealable plastic bag. In a medium bowl, stir together yogurt, lime zest and juice, honey, curry powder, coriander, onion, and mint. Season with salt and pepper. Pour marinade over lamb mixture; toss to coat. Let marinate, covered, in refrigerator at least 6 hours and up to 24. Soak skewers in water.
Thread skewers with lamb, others with zucchini, and others with summer squash; discard marinade. Season with salt and pepper.
Heat a grill pan to medium-high and grill lamb skewers until cooked to medium, about 4 minutes each side, and zucchini and squash skewers, turning frequently, 10 to 12 minutes. Remove from grill and serve immediately.
