Place the lentils, bay leaves, and 2 cups of the water in the Instant Pot. Secure the lid and set to Pressure Cook for 7 minutes.
Meanwhile, in a small bowl, whisk together the oil, parsley, lemon zest and juice, and 1/4 tsp of the salt. Set aside.
Coat 4 (6 oz) ramekins with cooking spray and crack 1 egg into each ramekin. Set aside.
Use a quick pressure release. When the valve drops, carefully remove the lid and drain the lentils (discarding the lentil water and 2 bay leaves). Return the lentils to the Instant Pot with the spinach and 1/4 tsp of the salt. Toss until the spinach is just wilted and divide it between 4 soup bowls. Cover to keep warm.
Add 1 cup of water to the pot, add a trivet and 3 ramekins. Stack the 4th ramekin on top of the other ramekins. Secure the lid, press the Cancel button, and reset the Pressure Cook button to 1 minute.
Use a natural pressure release for 1 minute, followed by a quick pressure release. When the valve drops, carefully remove the lid. Remove the ramekins and drain off any excess water that may have accumulated while cooking. Carefully run a knife around the outer edges of each egg to release from the ramekin easily.
Spoon equal amounts of the oil mixture on top of each serving of lentils and top with the eggs. Sprinkle with black pepper.