Stir together vinegar, 1/2 cup water, sugar, and 1 teaspoon salt in a saucepan; bring to a simmer over medium. Place carrots in a glass bowl. Add vinegar mixture; let stand 1 hour. Bring stock, lentils, and remaining 1/2 teaspoon salt to a boil in a saucepan. Cover, reduce heat to medium, and simmer until lentils are tender, about 45 minutes. Stir in kale. Remove from heat; cover and let stand until kale is slightly wilted, about 5 minutes. Stir together almond butter, lemon juice, sesame oil, soy sauce, and garlic in a bowl. Whisk in 1 tablespoon water. If necessary, whisk in remaining water, 1 teaspoon at a time, until desired consistency is reached. Drain carrots. Place 3/4 cup lentil mixture in each of 4 bowls. Top evenly with pickled carrots and avocado. Drizzle with almond sauce.