Using a mandoline or a sharp knife, cut the Brussels sprouts into really thin shreds. Rinse them with ice cold water and dry well in a salad spinner, or roll them in layers of paper towels. (This crisps and cleans the sprouts.)
In a large bowl, whisk together the lemon juice, olive oil, Parm, pepper, and salt. Add the Brussels sprouts, grapes, and almonds and gently toss.