Prep. Prepare a sous vide immersion circulator, such as Joule by ChefSteps, according to the manufacturer's instructions and set the water temperature for 131°F (55°C). Take the butter out of the fridge and let it come to room temp. Cut the lemon in half. Chop the parsley. Finely mince the garlic.
For the chimichurri butter, combine the butter, parsley, lemon juice, and garlic in a small bowl and blend well. Set aside until ready to use.
For the lobster, place the tails in a sealable freezer bag. Carefully submerge the freezer bag in the water bath until most of the air has been removed and then seal. Submerge the bag completely in the water bath and cook the lobster tails for 35 minutes.
Fire up. As the lobster tails near completion in the water bath, prepare a grill for 2-zone cooking. On a charcoal grill, place a chimney full of pre-heated charcoal briquets to one side of the grill's charcoal grate in order to create direct and indirect cooking zones. You want one side scorching hot and the other side at about 225°F (107°C). On a gas grill, adjust the temperature knobs so that one half of the grill is as hot as possible and the other half is approximately 225°F (107°C).
Remove the lobster tails from the freezer bag and run under cold water until the shells are cool enough to handle comfortably. Place the lobster tails on a sturdy cutting board with the softer bottom shell facing up. Use a sharp cleaver or chef’s knife to split each lobster tail in half lengthwise.
Grill. Place the halved lobster tails meat side down on the hot side of the grill. Grill until the meat is lightly charred, about 2 minutes. Flip the lobster tails over and continue to grill for another 2 to 3 minutes, basting with chimichurri butter. If the grill starts to flare up, move the lobster tails to the cool side of the grill to finishing basting with chimichurri butter.
While the lobster grills, place the lemon halves cut side down on the grill over direct heat and cook until lightly charred, 2 to 3 minutes. Set aside as you finish grilling the lobster.
Serve. Remove the lobster tails from the grill, plate, and brush once more with the chimichurri butter. Garnish with the parsley and serve immediately with the charred lemon for squeezing.
