Place the pork in the slow cooker with all the other ingredients. Cover and cook on low for 8 hours or high for about 4 hours, until the pork shreds easily with a fork.
Remove the pork from the cooker. Discard any fat. Using two forks, finely shred the meat. Return to the cooker to heat through in the juices.
To assemble, place the shredded lettuce on the bap bases. Top with the hot pork and juices, the onion and bap cap.