Marinate chops with vinegar, olive oil, minced garlic, salt, pepper, cumin, Italian seasoning, parsley, lemon juice and sesame oil. Refrigerate overnight if possible.
Bring marinated chops to room temperature.
Add oil and butter into a cast iron skillet over medium-high heat.
When skillet is hot, fry lamb chops for 5 minutes per side. Check for internal temperature >145 degrees F. Fry for additional 1-2 minutes if necessary.