Prepare a grill fire to 450°. We are using our Big Green Egg ceramic grill with lump charcoal and pecan chunks. 

Pat the steaks dry with paper towels. Coat with olive oil and dry rub on both sides.

Use kitchen shears to cut down the center of the shell to the tail with kitchen shears but do not cut through the fin. 

Add the butter to a pan with minced garlic and cook over medium heat, stirring occasionally for 5 minutes. Remove from heat, stir in dried thyme. Pour half of the butter into a bowl and reserve for serving. 

Brush garlic butter over the lobster tails. 

Place steaks onto the grill, cook 3 minutes with the grill closed. 

Flip the steaks and add the lobster tails. 

Close the grill and cook another 5 minutes. 

Use a digital meat thermometer to cook the steaks to desired temperature (we pulled ours at 130°) and lobster to 145°. 

Remove from grill. Rest for 10 minutes before serving. 

Remove lobster tails from the shells and serve with garlic butter and lemon slices.