If pork has a fat cap, trim the large cap away with a sharp knife. It is okay if you don't get it all!
Sprinkle spice rub over all sides of the meat, and dab meat on plate/cutting board to pick up any extra spice mix that fell around it.
Layer lime slices until bottom of crockpot is just covered, and set pork (fat cap side down) over limes. The limes will work to break any extra fat down quickly.
Pour barbecue sauce and apple cider vinegar over the meat and cover with lid. Do not latch the lid, if it has a locking capability! This will steam the meat, leaving it mushy and overcooked.
Cook on low for 6 hours or high for 4. Pork will be fall apart tender when ready.
Remove meat from slow cooker and shred with two forks. Serve on a bun with more barbecue sauce, on top of a baked potato, or in a tortilla.
Notes
*No more than 4 pounds for 2 people. If you're cooking for one, you may want to find a smaller piece (closer to three pounds). For families larger than 4, you may want to find just a bit larger, if. you plan on having leftovers.