I'm happy that you have asked me to assist you with your grandchild and hope that you can benefit from my many years of helping grandparents like you.
First, more girls her age are completely potty trained and if she is only having loose stools then I suspect she does have a dietary intolerance.
You can certainly start with lactose free milk but to be honest, kids her age don't really need to drink milk anyway. I would suggest though that you first take a look at a link I'll post below regarding a group of substance/food/carbohydrate intolerances that are recognized as being almost as common as lactose intolerance. This group contains ingredients in many foods and juices as well as other common items such as gum, candy, etc.
Here is the link to take a look at and I see that your question has been posted for some time so I'll exit chat and allow you time to take a look at this information and then if you have any questions just let me know.
I'll watch for your return to chat.
Did you take a look at that article as it explains why so many people have irritable bowel syndrome but think there is nothing they can do for it or their child. Lots of people get on gluten-free diets and get better thinking that they have celiac disease when really all they have is an issue with one or more of the FODMAPS group of foods, additives, and other substances.
Perhaps you are away from your computer, as I have been, so please let me know what questions you have. I'll be with my grandchildren for a couple of hours but will check back here when I return.
I see you reposted your question and rated my answer as poor but I think you failed the purpose of the link I cited above. It is meant as a guide to eliminating from her diet those foods on the chart included in this article that she consumes daily to see which of the substances are causing her problem. I agree that changing diaper all day is not a solution and that is NOT what I suggested. It is going to require that her caretakers take a close look at all of the foods on this chart and eliminate them from her diet all at once or at least a few at a time. Lactose is a good start but not likely to the the sole cause of her problem.
Even consuming a little apple juice (fructose and sorbitol) can cause diarrhea as can chewing a couple of sticks of sugarless gum? All I can do on a website like this is give you some guidelines as to how to approach her problem but ultimately you and other caretakers are going to have to manage her diet to find out what the cause is and eliminate it from her diet forever.
I hope you will reconsider the poor rating as that is not something I'm accustomed to as one of the leading pediatric experts on JustAnswer. Without knowing specifically everything in her diet I simply cannot be more specific than this but you now have the guidelines to follow in eliminating potential causes of what almost certainly is her problem, which it the foods and beverages she consumes daily.
I have printed the article you linked me to but it is hard to sort all the info.. Have you ever had patients like this before? She loves scrambled eggs, pancakes, grapes, apples and oranges. why do you think it is her diet and something not more internal?
So I am to assume my 4 yr. old has IBS and certain foods are causing her to poop 24/7 in her diaper/panties. I will certainly talk with her mother and we will look at her diet closely. You said something that threw me off. "Four year olds don't really need to drink milk anyway." What about getting calcium and Vitamin D? We have tried giving her gatoraid liquids and that seems to help some but the problem is still there. She's not a big eater so cutting out what she will eat may be difficult. But it will be worth it if we can get to the bottom of her problem. She is miserable and we are desperate for help for her.