In a large saucepan, heat olive oil over medium heat. Add the diced onion and sauté until translucent, about 5 minutes.
Stir in the minced garlic and grated ginger, cooking for an additional 1-2 minutes until fragrant.
Add the diced carrot and bell pepper to the pan, stirring gently for another 5 minutes until slightly softened.
Mix in the curry powder, turmeric, and cumin, stirring well to coat the vegetables in the spices. Cook for 1-2 minutes to enhance the flavors.
Add the rinsed red lentils, diced tomatoes, coconut milk, and vegetable broth to the pan. Stir everything well to combine.
Bring the mixture to a gentle simmer. Reduce heat to low, cover, and let it cook for 20-25 minutes, or until the lentils are tender and the curry has thickened, stirring occasionally.
Season with salt and pepper to taste. If desired, adjust the thickness by adding more broth or water.
Once cooked, remove from heat and let it sit for a few minutes. Serve warm, garnished with chopped cilantro and lime wedges on the side.