I'm not sure which restaurant you are asking about (Chef Mickey's?), but I can tell you that Disney does an outstanding job of catering to dietary restrictions. First, make sure that you include a notation about your son being lactose intolerant in your reservations. At any counter service restaurant, you can ask to see a list of ingredients.
You are welcome to email Disney directly to ask specific questions, too:
specialdiets@disneyworld.com As for ice cream, many of the restaurants offer the option or rice or tofu ice cream. At the ice cream carts, there are fruit bars and Itzakadooze ice pops, which I believe are free of lactose.
I'd also encourage you visit www.lauraschmittne.com and do a search for
Walt Disney World for a thorough review of dairy free food offerings.