Rinse the lentils and place them in a saucepan with 2 cups of water. Bring to a boil, then reduce heat and simmer for 20 minutes until tender. Drain any excess water and set the lentils aside.
Heat the olive oil in a large skillet over medium heat. Add the diced onion and green bell pepper. Cook for 5 minutes, stirring occasionally, until the vegetables soften.
Stir in the minced garlic and cook for 1 minute until fragrant.
Add the cooked lentils, tomato sauce, tomato paste, brown sugar, chili powder, mustard, salt, and black pepper to the skillet. Stir everything together until well combined.
Simmer the mixture for 10 minutes, stirring now and then, until the sauce thickens and coats the lentils evenly.
Split the whole wheat buns and spoon the lentil mixture onto each bottom half. Place the top halves on and serve right away.