Combine 1/2 cup boiling water, bulgur, and 1 tablespoon lemon juice in a medium bowl. Let mixture stand for 15 minutes. Add chickpeas, cucumber, celery, diced red onion, 1 1/2 tablespoons feta cheese, and dill; toss gently to combine.
Combine 1 1/2 teaspoons lemon juice, olive oil, salt, and pepper, stirring with a whisk. Drizzle over bulgur mixture, and toss gently to coat. Cover and chill.