In a medium pot, combine brown lentils with water and bring to a boil. Reduce to a simmer, cover, and cook for 25-30 minutes until tender. Drain excess water and set aside.

In a skillet, heat olive oil over medium heat. Add onion, garlic, carrot, and celery, sautéing for 5-7 minutes until softened. Remove from heat and let cool.

In a large mixing bowl, coarsely mash the lentils. Stir in the sautéed vegetables, rolled oats, breadcrumbs, flax egg, soy sauce, tomato paste, thyme, paprika, salt, and pepper. Mix well.

Line a loaf pan with parchment paper or grease it. Press the lentil mixture into the pan firmly and smooth the top, creating a slight indentation.

In a small bowl, whisk together ketchup, maple syrup, and balsamic vinegar. Pour the glaze over the meatloaf, spreading evenly.

Preheat oven to 375°F (190°C) and bake for 45-50 minutes until golden brown. Check for doneness with a toothpick.

Let the meatloaf cool in the pan for 10 minutes. Transfer to a cutting board, slice, and serve warm.