In a pitcher, combine the sliced cucumber and cold water. Refrigerate to infuse while you prepare the rest of the meal.
Heat a large pot over medium heat. Once hot, add the olive oil. Sauté the onion, carrots, celery, and garlic for about 5–7 minutes, or until they begin to soften.
Stir in the chicken broth, canned diced tomato, fresh thyme sprigs, and brown lentils. Bring to a simmer and cook for 20–30 minutes, until the lentils are tender and the flavors are well developed.
Check the lentils for doneness; they should be tender but not mushy. Remove the thyme sprigs before serving.
Ladle the lentil soup into bowls and serve with cheese and crackers, and cucumber water.