Add 2 cups of water, lemon slices, garlic slices, and rosemary to a 6-quart Instant Pot.
Place the steaming rack on top.
Drain the artichokes by turning them upside down and shaking off the excess water.
Place the artichokes on top of the steaming rack, top side facing up.
Make sure that the release valve is in the "Sealing" position.
Place the lid on the Instant Pot, turn and lock the lid.
Press "Manual" button on the Instant Pot on high pressure, and then set the timer to 15 minutes using the "+" or "-" buttons.
It will take about 10 to 15 minutes for the pot to heat up and build up the pressure. You will see some steam release from the lid, and then the time will start on the display.
Once the display indicates "On" and begins the countdown at "10", the Instant Pot will beep when the cycle is complete.
Cover the steam release handle with a towel to avoid splattering. Natural release for 15 minutes then release the pressure from the pot by sliding the steam release handle to the "Venting" position, releasing all of the steam until the float valve drops down.
Carefully open the lid and use tongs to remove the artichokes.
The artichoke is ready when the leaves can be easy to remove and the meat is tender.