Set Instant Pot to sauté mode. Add olive oil, onion, and garlic; cook until fragrant.

Add chicken breast and chicken broth. Pressure cook for 12–15 minutes, then shred chicken.

Switch back to sauté mode, bring broth to a boil, and add orzo. Cook until orzo is tender. (About 7 minutes)

In a separate bowl, whisk eggs, lemon juice, and zest. Slowly whisk in a few tablespoons of hot broth to temper the eggs.

Stir the egg-lemon mixture back into the soup. Turn off sauté mode.

Add spinach and stir until wilted. Season with salt and pepper to taste. Serve warm.