Heat butter and olive oil in a saucepan over medium heat. Add onion, carrot, celery, and salt; cook and stir until vegetables are softened and onion is translucent, about 10 minutes.
Reduce the heat to low and add thyme sprigs and pepper. Stir in lentils until well coated. Add chicken stock and bring to a gentle simmer. Cover and cook, checking occasionally, until lentils are tender and have absorbed all the liquid, about 35 minutes.
Remove from the heat and discard thyme stems. Stir in parsley and vinegar. Season with salt and pepper as needed.