In large resealable plastic bag, combine lime juice, fish sauce, sesame oil, jalapeño pepper and garlic. Add pork roast and move marinade around roast to coat. Seal bag and refrigerate for at least 4 hours or up to 12 hours.
Using a vegetable peeler, peel all of the cucumber into long strips and place into a large bowl. Repeat with carrot. Add coriander and mint and toss with vinegar; set aside.
Heat both sides of the barbecue on high. Place pork roast on grill, reserving marinade; brown roast on all sides. Turn one side of the barbecue off and turn the other side to medium-low heat. Place roast on unlit side. Close lid and cook for 45 minutes, adjusting the heat as necessary to keep temperature around 325°F, and brushing occasionally with all of the reserved marinade.
Turn roast over and cook for about 1 hour and 30 minutes or until meat thermometer inserted in centre registers 155°F. Place roast on cutting board and tent with foil for 10 minutes before slicing.