Step 1Place the lentils in a large fine-mesh sieve and rinse under cold running water. Transfer them to a large (3-quart) heavy-duty saucepan, cover with cold water, and bring to a boil over high heat. When the water boils, remove the saucepan from the heat. Transfer the lentils to a fine-mesh sieve and drain over the sink. Rinse the lentils under cold running water. Return the lentils to the saucepan, add the chicken stock, and bring just to a boil over high heat.
Step 2Reduce the heat to a simmer. Using a slotted spoon, skim off any impurities that rise to the surface. Once the liquid is clear of impurities, add the carrot and onion. Simmer gently, uncovered, over low heat until the lentils are cooked yet still firm in the center, about 30 minutes. (The cooking time will vary according to the freshness of the lentils: The fresher they are, the more quickly they will cook.) Remove and discard the onion and carrot.
Step 3Transfer the lentils to a fine-mesh sieve set over a bowl. Drain, reserving the cooking liquid. Transfer 1 cup of the reserved liquid and 1 cup of lentils to the bowl of a food processor; puree.
Step 4Return the whole lentils and the puree to the saucepan. Add the sea salt and black pepper. Add the butter and the minced truffle and warm over low heat just until the flavors are blended. Taste for seasoning.
Step 5Transfer to small warmed plates, sprinkle with the truffle triangles, and serve immediately.