Mix lime juice, soy sauce, garlic, tamarind paste, sugar, and sambal oelek together in a bowl. Whisk for 1 minute. Poke pork tenderloin with a fork or knife and place in a large resealable plastic bag. Pour marinade into the bag and seal while pressing out the air. Marinate in the refrigerator 8 hours to overnight for best results.
Preheat an outdoor grill for high heat and lightly oil the grate.
Remove pork loin from the bag and sear on the preheated grill, 1 to 3 minutes per side. Move to indirect heat until cooked through, 20 to 30 minutes more, depending on thickness.
