Add olive oil to Instant Pot and turn on Saute. Add the onion, carrot and bell pepper and saute until softened, about 4 minutes. Add the garlic and cook, stirring, for 30 seconds. Press Cancel to turn off the Saute function.
Add the lentils, tomato sauce, ketchup, maple syrup, apple cider vinegar, mustard, chili powder, salt, pepper and broth to the pot. Stir, scraping up any bits that might be stuck to the bottom of the pot.
Close the Instant Pot lid and turn the steam release valve to the sealing position. Pressure cook at high pressure for 5 minutes. The Instant Pot will take about 15 minutes to reach pressure and then the cook time will begin counting down.
When the cook time ends, allow the pressure to release naturally for 10 minutes by just leaving the Instant Pot alone. Then, carefully use the handle of a long spoon to turn the steam release valve to the venting position. Wait for all of the steam to escape and the pin to drop down and then open the Instant Pot lid.
Stir the sloppy joe mixture and serve on toasted burger buns.