Preheat the oven to 375 degrees F with 2 racks set in the middle. Stir together 1/4 cup water, 1 tablespoon of the oil, 2 tablespoons red wine vinegar, thyme, garlic and 1/4 teaspoon salt together in a 2-quart baking dish. Add the beets and stir to coat in the liquid. Cover the baking dish with aluminum foil and bake in the upper rack of the oven until the beets are fork-tender, about 1 hour, stirring the beets once halfway through the cooking time.
Meanwhile, spread the walnuts on a baking sheet and toast on the lower rack of the oven until slightly darkened in color and fragrant, 12 to 15 minutes. Remove from the oven and cool completely. Finely chop 3 of the toasted walnuts and reserve for garnish.
Remove the thyme from the baking dish and discard. Cool the beets and cooking liquid slightly, about 10 minutes. Add the beets, cooking liquid (along with the cooked garlic), whole toasted walnuts, lentils, remaining 2 tablespoons olive oil, 3/4 teaspoon salt and 1/4 teaspoon pepper to a food processor. Process until smooth, scraping down the sides of the bowl as needed. Season with the remaining 1 tablespoon red wine vinegar if desired.
Transfer the dip to a small serving bowl and garnish with the reserved walnuts. Serve with pita chips and vegetables.
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