Add the barbecue seasoning mix, ketchup, brown sugar, and cider vinegar to a medium bowl. Stir until thoroughly combined and set aside.
Set the Instant Pot to the SAUTÉ function. Add the oil and allow it to heat.
Place the lamb shoulder pieces in the pot. Sear for about 5 minutes, turning once, until the outside is lightly browned.
Pour in the water, scraping the bottom of the pot gently to loosen any browned bits.
Pour the prepared barbecue sauce mixture evenly over the lamb.
Secure the Instant Pot lid and set the pressure valve to the sealing position.
Pressure cook on high for 60 minutes. Once cooking is complete, carefully release the pressure according to your Instant Pot manufacturer's instructions.
Check the lamb. It should be very tender and pull apart easily with a fork. If necessary, pressure cook for another 10–15 minutes.
Transfer the meat to a large bowl and shred it using two forks.
Return the shredded lamb to the pot and stir until thoroughly coated with the sauce.
Serve your Instant Pot Pulled Lamb warm on sandwich rolls, in wraps, or with your favorite side dishes.