Mix the milk and oats. Blend at high speed for 3 minutes. Sieve to get rid of solids (optional). Add sugar to taste.
Chill in the freezer (it has to be very cold, or it will curdle). If you need to store for a few hours, chill in the fridge instead of the freezer. Remove from the freezer and add the ice, stir. Slowly pour the lime juice into the oatmeal mix stirring constantly.