Set your grill to medium-high heat, about 400–450°F.
Using kitchen scissors, cut along the back of each lobster tail (the side without the little spikes), stopping just before the tail fins, and gently pull apart the shell to expose the flesh.
In a separate small bowl, mix together the melted butter, garlic, lemon juice, salt, and pepper. Reserve half this butter mixture in a separate clean bowl for serving.
Brush the lobster tails with half of the butter mixture.
Place the tails directly on the grill grates, shell side down. Grill for 4-5 minutes, then flip and grill the other side for 3-4 minutes, until the flesh is white and opaque, the shell is bright red, and the internal temperature reaches 135–140°F. Be careful not to overcook.
Serve immediately, drizzling with the reserved (clean) garlic-lemon butter.