Anyone can develop secondary lactose intolerance
after an episode of gut infection. This will be temporary.
So stop milk for few days till she is completely alright.
But a 3 yr old should get a nutritious food and milk should be restricted to 2 glasses per day.
During this diarrheal episode, give her curd(yoghurt), soups, mashed potato, rice based food items, cooked dal etc. Curd is very good as it has probiotic
bacteria naturally additional to the nutrients of milk too.
You may give her soyamilk too.
Hope you find my answer helpful.