Pour water into Instant Pot®and add the trivet.
Place whole spaghetti squash onto the trivet.
Close the lid, turn the knob to Sealing.
Press Manual or Pressure Cook button and adjust time to 20 minutes.
When the timer beeps, turn the knob from sealing to venting, then remove the lid and carefully transfer the spaghetti squash to a cutting board. Let cool for 10 minutes.
Carefully slice the spaghetti squash in half. Cutting the squash through the stem will result in shorter strands while cutting in the middle will result in longer strands. Scoop out the seeds from each halve, then using tongs or a fork, gently scrape and pull the spaghetti squash out of the shell into a strainer. Push the squash against the sides of the strainer to remove as much liquid as possible, then measure two cups, packed, for the dish and reserve the rest. This should be about half the squash.
Drain and rinse out the Instant Pot® liner and place it back in the base. Press the Saute button and adjust to low.
Add 2 teaspoons lemon zest, heavy cream, and salt to the Instant Pot® and stir to combine. Add spaghetti squash and toss to coat. Slowly stir in the lemon juice and transfer to a serving bowl.
Swirl the spaghetti squash into a tall mound, then top with freshly cracked black pepper, fresh parsley, parmesan cheese, and the remaining lemon zest.