Set the Instant Pot to SAUTE mode and heat the olive oil. Add the chopped onion, carrots, and celery, cooking for 4 to 5 minutes until softened.
Stir in the minced garlic and cook for an additional 1 minute until fragrant.
Add the rinsed lentils, diced tomatoes with their juices, and vegetable broth. Stir well to combine, then press cancel to turn off the SAUTE mode.
Secure the Instant Pot lid, set the valve to the sealing position, and cook on Manual High Pressure for 15 minutes.
Allow the Instant Pot to do a natural pressure release for 10 minutes, then carefully switch the valve to venting to quickly release any remaining pressure.
Open the lid and stir in the fresh spinach. Let the soup sit for 1 to 2 minutes until the spinach is completely wilted. Serve hot.