Hi Zoe and welcome to the Disney Parks Moms Panel.
The Walt Disney World Resort is committed to offering a wide range of culinary and dietary options for its Guests. By substituting different ingredients and approaches, most Disney chefs, restaurants and quick-service locations can accommodate many common food allergies including lactose.
As far as I am aware, it is possible to purchase lactose free soy milk at all of the Walt Disney World Resort hotels.
In order to put your mind at rest, I would recommend that you email Special.Diets@DisneyWorld.com prior to your arrival at the Walt Disney World Resort to notify Disney of your son's allergy and at the same time, to enquire about all of the locations where lactose free milk / lactose free ice cream is available.
I would also suggest that you make a note of your son's allergy when making all of your Advance Dining Reservations.
You can read more about
Special Dietary Requests on the Walt Disney World website.
Wishing you a magical holiday filled with memories which will last a lifetime!
Emma