Let the lamb chops rest at room temperature for 20–30 minutes for even cooking.
Pat the chops dry with paper towels. Season both sides with salt, black pepper, and red pepper flakes if using.
Heat olive oil in a cast-iron skillet over medium-high heat until shimmering.
Add the lamb chops in a single layer and sear for 3–4 minutes per side until golden brown.
Reduce heat to medium. Add butter, minced garlic, and rosemary to the skillet.
Spoon the melted garlic butter over the lamb chops for 1–2 minutes.
Remove the chops once the internal temperature reaches about 130°F for medium-rare.
Tent loosely with foil and let rest for 5–7 minutes.
Finish with fresh lemon juice just before serving.
Juicy Garlic Butter Lamb Chops are best served immediately while warm and tender.