Start by preparing the lobster tails. Use a sharp knife to cut the top shell of the lobster tail down the center, stopping just before the tail fin. Carefully pry the shell open slightly and lift the lobster meat upwards so it rests on top of the shell.
In a small bowl, melt the butter. Add the olive oil, minced garlic, lemon juice, paprika, salt, and pepper to the melted butter. Mix well.
Preheat your grill to medium-high heat.
Brush the lobster meat generously with the butter mixture, reserving some for later.
Place the lobster tails on the grill, shell side down. Grill for about 5-7 minutes, basting with the reserved butter mixture halfway through, until the meat is opaque and has grill marks.
For added flavor, you can grill the lobster tails for an additional 1-2 minutes meat side down to get a nice char.
Remove the lobster from the grill and serve immediately with lemon wedges and any remaining butter sauce for dipping.