In a bowl, combine olive oil, lemon juice, garlic, cumin, paprika, oregano, salt, and black pepper to make the marinade.
Add lamb cubes to the marinade, toss to coat, cover, and refrigerate for 1–2 hours.
Soak wooden skewers in water for at least 30 minutes if using wooden skewers.
Thread marinated lamb cubes onto skewers evenly.
Preheat grill or grill pan over medium-high heat.
Grill skewers for 4–6 minutes per side or until lamb reaches desired doneness.
While lamb is grilling, combine Greek yogurt, mint, lemon juice, honey, salt, and pepper to prepare the dip.
Serve grilled lamb skewers hot with mint yogurt dip on the side.