Combine the lentils and rice in a large pot with the vegetable stock. Bring to a boil over medium-high heat. Once it has begun to boil, lower the heat to a simmer, cover the pot and allow to cook until the water has been absorbed, about 45 minutes.
While the lentils and rice are cooking, heat the oil in a pan over medium-high heat. Add the onion and cook until it begins to brown, about 5 minutes. Add the garlic and carrots, and cook until the carrots are tender, about 10 more minutes.
Preheat your oven to 350° and line a loaf pan with parchment paper.
In a large bowl, mix together the cooked lentils and rice, the vegetables, and the rest of the ingredients. Mash as little as you can, so the lentils don’t lose their shape.
Transfer the mixture to the prepared loaf pan, and bake until firm and lightly browned on top, about 45 minutes.