Preheat the grill to medium-high heat.
Prepare the lobster tails by cutting them in half lengthwise.
In a small saucepan, melt the butter and mix in Cajun seasoning, olive oil, and lemon juice.
Brush the lobster meat with the Cajun butter mixture.
Sprinkle with salt and pepper.
Place the lobster tails on the grill, cut side up.
Grill for 8-10 minutes, basting with remaining butter mixture halfway through.
Remove from the grill and let rest for a few minutes.
Serve with additional lemon wedges and the remaining Cajun butter.
