Take the pork loin out of the refrigerator 30 minutes before cooking, to allow it to come to room temperature.
Preheat your grill to 400 degrees for direct heat.
Place your lemon, cut side down on the grill and allow it to get a good char on it. Once softened and browned, remove the lemon from grill and allow to cool slightly.
Grill the pork loin for 5 minutes per side, until it reaches 140-degrees, about 20 minutes total. Remove from grill and let it rest for 10 minutes while you prepare the chimichurri.
In a food processor or blender, add the oregano, mint, garlic, anchovy, and capers. Squeeze in the juice from the charred lemon halves and add the olive oil. Pulse until combined but not entirely smooth.
Slice the pork tenderloin and serve the charred lemon chimichurri drizzled on top with the remaining sauce served on the side.