Prepare the lobster tails by butterflying: use kitchen shears to cut down the top center of the shell toward the fin, then gently separate the meat from the shell leaving it attached at the base.
Lift the meat up and lay it over the shell for presentation, or leave it inside the shell if you prefer to cook that way.
Brush the exposed lobster meat with the melted butter or ghee and season with salt and pepper or Cajun seasoning.
To bake: preheat the oven to 400°F, place prepared tails on a rimmed baking sheet, and bake small 3–4 oz tails about 10 minutes or larger 6–8 oz tails about 20 minutes; check with a meat thermometer and add time if needed.
To grill: preheat the grill to 425°F, grill cut-side-down until lightly charred (small tails ~3 minutes, large ~5 minutes), then flip and finish cooking (small +1 minute, large +2–3 minutes).
To steam: add 1 inch of water to a 6-quart pot with a steaming basket, bring to a boil, place tails in the basket, cover, and steam small tails 5–6 minutes or larger tails 8–9 minutes.
To air fry: preheat the air fryer to 380°F, place tails cut-side-up in the basket, and air fry small tails 3–5 minutes or larger tails 5–7 minutes.
Serve immediately with extra melted butter or your preferred condiments.