Most of the Wal-Mart's nearby as well.
To be sure, do a yahoo search on "Supermarkets" in/around Lake Buena Vista before you arrive and call to be sure.
Park restaurants and gift shops will probably NOT have it, but they do offer soy & rice milks.
Therefore you will either need a car or a towncar stop.
Our little boy is/was lactose-intolerant (his Dad's reactions to those Mickey bars aren't so pretty either) so we've gone through this.