Set Instant Pot to Sauté mode. Add 4 tablespoons unsalted butter to Instant Pot insert and let butter melt completely.
When butter has melted, add 1 cup chopped white onion and 2 tablespoons minced fresh garlic to insert. Stir to incorporate, then sauté aromatics approximately 5 minutes or until onions are soft and translucent.
Add 1 ½ pounds boneless, skinless chicken breasts to insert. Sauté chicken pieces, stirring occasionally, approximately 5 minutes or until chicken pieces are opaque on all sides.
Add 1 ½ cups long-grain white rice, 3-4 cups chicken broth (3 cups for firmer rice; 4 cups for softer, soupier rice), and 2 tablespoons fresh lemon juice to Instant Pot insert. Stir to fully incorporate ingredients, making sure to scrape bottom of insert to loosen any stuck bits of onion or garlic.
Secure lid on Instant Pot with valve in Sealing position. Set Instant Pot to Manual High Pressure mode and set cook time to 8 minutes. Instant Pot will pressurize and then 8-minute cook time will begin.
When 8-minute cook time ends, Natural Release internal pressure 2 minutes. Note: Do not release pressure longer than 2 minutes or rice can overcook.
After 2-minute Natural Release, carefully Quick Release any remaining pressure and remove lid. Use caution as any escaping steam will be incredibly hot.
Stir chicken and rice mixture well. Note: If mixture contains excess standing liquid after pressure cooking, set Instant Pot to Sauté mode and stir mixture until excess liquid has fully incorporated into rice.
Taste mixture and add 1 cup shredded fresh parmesan, 1 ½ teaspoons salt, and ¼ teaspoon black pepper. Stir until additions are well incorporated, then taste mixture again and add more parmesan, salt, pepper, or lemon juice if desired.
When satisfied with flavor of chicken and rice mixture, portion mixture into preferred servings. Garnish with additional parmesan cheese if desired and serve warm.