Prepare the compound butter by mincing garlic, chopping parsley and shallot, mixing all with softened butter until even. Form into a log on parchment and freeze for 10 minutes.
Preheat oven to 375°F and grease a baking pan lightly.
Prepare lobster tails by cutting shell lengthwise and loosening meat; place meat-side up on the baking pan.
Pat steaks dry, season evenly with salt and pepper on both sides.
Heat skillet over high heat, add olive oil and sear steaks for 1-2 minutes per side until golden crust forms.
Place lobster tails on the pan, top each with a pat of compound butter and drizzle with fresh lemon juice.
Transfer lobster pan and skillet with steaks into oven; bake lobster for 6-8 minutes until opaque and steaks to 125-145°F internal temperature.
Remove both from oven; rest steaks for 5 minutes on a warm plate.
Serve lobster tails and steaks on plates, topping steaks with remaining compound butter and garnishing with lemon wedges.