Combine mushrooms and celery in a large bowl. Combine oil, 1 tablespoon juice, and 1/4 teaspoon salt in a small bowl, stirring well with a whisk. Taste oil mixture; add remaining 1 tablespoon juice and 1/4 teaspoon salt, if needed.
Add oil mixture to mushroom mixture; toss gently. Taste again; if any remaining juice and salt have not yet been added, stir in, if needed. Top with cheese.