Preheat oven to 350°.
Combine water and lentils in a small saucepan; bring to a boil. Reduce heat; simmer 20 minutes or until lentils are soft.
Combine 2 tablespoons vinegar, mushrooms, shallots, and garlic in a bowl. Place mushroom mixture on a jelly-roll pan, and bake at 350° for 15 minutes.
Combine lentils, mushroom mixture, 2 tablespoons vinegar, walnuts, basil, salt, and pepper in a food processor; process until smooth. Serve with baked tortilla chips or pita bread, if desired.