Seems like something simple that one could have asked a doctor.. "My kid keeps licking their hands.. any ideas?"

Also even though the article the mother seems to think that they have gotten to root cause.. there may be more of a cause.

Dry hands is often because of the compulsive action of washing ones hands too much. So now there are 2 compulsions washing hands and licking hands to keep them dry.. By replacing licking hands with moisturizer you will still have 2 compulsions.. cleaning hands and moisturizing too much..

A 2 second google search will also bring up thousands of pages about kids licking hands.