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 lightly oil a loaf pan, or 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 a little as you, so the lentils lose their shape.
Transfer the mixture to the prepared loaf pan, and bake until firm and lightly browned on top, about 45 minutes.