Roughly chop the celery. Chop the apple, keeping the skin on.
Place the celery, apple, and water in a blender. Blend on high until pureed and a juice forms.
Pass the juice through a fine mesh sieve or a nut milk bag to strain out the pulp. Discard the pulp (or use: see ideas above). Stir in the fresh lemon juice (add more if desired). Drink immediately over ice, or chill before drinking.