Select "Sauté" on the Instant Pot. Heat olive oil and sear chicken breasts until they're golden brown. Remove them and set them aside.
In the same Instant Pot, sauté chopped onion and minced garlic until they're fragrant and tender.
Stir in long-grain rice, lemon pepper seasoning, dried thyme, salt, and black pepper. Cook for a few minutes until the rice is lightly toasted.
Pour in chicken broth, lemon zest, and lemon juice. Stir well to combine all the flavors.
Gently return the seared chicken breasts to the Instant Pot.
Close the Instant Pot lid and set it to "Pressure Cook" for 6 minutes. Allow a natural release for 5 minutes, followed by a quick release.