Fill a medium pot halfway with cold water. Add carrot, celery, onion, lentils, peppercorns, and red wine vinegar. Bring to a boil.
Place the tomatoes into a strainer to drain; discard liquid. Set aside.
Check the lentils after about 20 minutes, although they may need closer to 30 minutes. Not all lentils cook in the same amount of time, so you will need to taste one. They should be slightly al dente, not mushy and falling apart but not hard. When the lentils are almost done, add 1 teaspoon coarse salt. Stir.
Drain the lentils, rinsing in cold water to stop the cooking. Pick out and discard the carrot, celery, and onion. Place lentils into a large bowl.
Add drained tomatoes and tuna with its oil. Add the thyme, cayenne, olive oil, and vinegar. Stir. Season to taste with more coarse salt, at least ½ teaspoon.
Drizzle with additional olive oil; garnish with a sprig of fresh thyme and a small pinch of Maldon salt.
Recipe posted with permission from Kosher By Design Brings It Home: picture-perfect food inspired by my travels, by Susie Fishbein