Season lamb chops generously and allow them to rest at room temperature. Split lobster tails lengthwise and season lightly. Prep all aromatics before cooking to keep the process smooth.
Heat butter and olive oil in a wide pan, then sauté shallots until soft. Add garlic and herbs, then deglaze with white wine and reduce slightly. Sear lamb chops in the sauce, basting continuously, until cooked to desired doneness. Remove and rest.
Using the same pan, spoon sauce over lobster tails and cook gently until just opaque and tender. Finish with lemon juice and parsley, then serve immediately.
Notes
Use a thermometer for both proteins to avoid overcooking