To make the Tzatziki Sauce, in a small bowl or jar, combine all sauce ingredients and refrigerate until ready to eat.
To make the Chicken Bowl, to the Instant Pot®, add oil, butter, lemon juice and zest, broth, rice, oregano, garlic, salt, and black pepper. Stir to combine. In a small bowl, toss the chicken in lemon pepper, then spread evenly over rice.
Close the lid; turn the knob to Sealing.
Press Manual or Pressure Cook button and adjust time to 10 minutes.
When the timer beeps, allow 5 minutes to naturally release the pressure, then remove the lid.
Scoop the chicken and rice into a serving bowl, then top with tomato, bell pepper, feta, onion, cucumber, and olives. Serve immediately with Tzatziki Sauce.