Place oil in a multi-functional pressure cooker (such as Instant Pot) and select Saute function. Add onion, bell pepper, and carrot; cook and stir until the onion has softened and turned translucent, about 5 minutes. Stir in garlic and saute until fragrant, about 1 minute. Cancel Saute function.
Add chicken broth, lentils, zucchini, eggplant, diced tomatoes with juice, parsley, cumin, and salt to the pot. Close and lock the lid. Select high pressure according to manufacturer's instructions; set timer for 20 minutes. Allow 10 to 15 minutes for pressure to build.
Release pressure carefully using the quick-release method according to manufacturer's instructions, about 5 minutes. Unlock and remove the lid. Stir in lemon juice and zest.