Use a serrated edge knife to cut an inch off the top of the artichokes and cut off the stems. Rub the half lemon over the artichokes where they've been cut to prevent browning. Use scissors to trim any sharp tips from the tips of the  leaves. 

Pour 1 1/2 cups water into the Instant Pot with the metal insert in place. Set the artichokes in the pot, stem-side-up. Cover and set to Manual/High for 13 minutes with the vent closed. 

Release the steam with care and open the pot. Test to see if the artichokes are done by tasting a leaf or two and inserting the tip of a knife in the stem. It should slide in with relative ease. If they're not quite done, cook another 1 to 2 minutes.

Whisk together the olive oil, melted butter, lemon juice, chives, and salt. Serve with the artichokes.