Rinse artichokes under cold water, then pat completely dry. Remove any small artichoke petals from base. Using a sharp knife, cut away stem, then cut off top 1" of artichoke. Using scissors, trim thorn tips off all petals. Rub lemon slices all over outside of artichoke.
Add lemon slices from step 1, garlic, and water to Instant Pot. Insert trivet, then stand artichokes upright in Instant Pot.
Cook on Manual High Pressure for 12 minutes (for small to medium sized artichokes) or 14 minutes (for large artichokes).
When time is up, Quick Release pressure and carefully remove lid. Remove hot artichokes from Instant Pot using tongs.
Serve with a simple dip of melted butter and mayonnaise. (Optional)