This only happens, when there is more milk in the stomach...then it can reasonably digest. The problem isn't the lemonade. The problem, is your child is drinking more milk then his stomach can handle or digest, in a reasonable amount of time. If he drinks less milk, an amount he can digest fully, then he likely won't be upset from lemonade. His stomach acid can do the same thing as lemonade. If there is too much milk, the stomach acid will have the same effect.
Short story long, LESS MILK.
**Oh, he's vomiting? Yeah...it should only make his stomach upset. He shouldn't really be vomiting. Are you sure he isn't sick...or drinking WAY too much milk, and it's just messing up his gut balance? How much milk does he drink in a day?