It's worth using that special bottle of olive oil and seeking out Parmigiano-Reggiano, which is bolder than basic Parm, for this simple salad. Use a mandoline to shave the veggies if you have one.
Combine cucumber, celery and radishes in a large bowl. Whisk oil and lemon juice in a small bowl or combine in a half-pint mason jar.
Just before serving, drizzle the dressing over the salad. Serve sprinkled with lemon zest, cheese, salt and pepper. Garnish with celery leaves, if desired.