Combine the lentils and water in a pot and bring to a boil. Reduce the heat to medium, cover, and simmer until soft, 30 minutes. Set aside, do not drain.
Heat the oil in a skillet over medium heat. Add the mustard seeds. When they begin to pop, add the onion, garlic, chiles, and ginger and cook until softened, 5 minutes. Stir in the tomatoes and cook 2 minutes. Stir in the sambar powder, coriander, cayenne, cumin, salt, and garam masala. Add the carrots, cauliflower, green beans, and eggplant. Cover and cook for 5 minutes to soften.
Add the vegetable mixture to the reserved lentils, cover, and simmer until the vegetables are soft, 20 minutes. Add the lemon juice and cilantro and cook 5 minutes longer.