If the lobster tails are frozen, leave them in the refrigerator to thaw overnight. Then, place them on your countertop to completely thaw before grilling.
Heat your Foreman Grill to high, approximately 5 minutes.
While the grill is heating, place the tails shell side down on a cutting board. Using kitchen shears cut the thick membrane that covers the flesh down the length of the tail. Flip the tail over and cut it in half lengthwise right through the shell. You will need a large, sturdy chef’s knife or cleaver to get through the shell. Repeat with the other tail.
Cut the butter into small pieces. Place the pieces of butter between the shell and the flesh along the length of each tail section. This will take a little effort using your fingers. You can wear disposable gloves for this if it feels strange to you.
Coat the bottom section of your grill with olive oil. Place the lobster tail pieces, shell side down, on the hot grill. Close the top. Cook for approximately 9 minutes until the flesh is just opaque and milky in color.
Notes
As the lobster cooks the butter will melt and baste it. The shell acts as a vessel to retain the moisture in the flesh. Place the cooked lobster on your cutting board to cool a bit while you get started on the rolls.