A late fee should only be charged if a written agreement outlines this possibility. Some states have a cap on how much can be charged for a late fee; check the state laws regarding the maximum that can be charged.
If there is no written agreement regarding late fees, there must be a notice provided to indicate that late fees may be charged; the notice must also outline those specific terms. If a late fee is charged to someone who knew nothing about that possibility, that person may not be legally responsible for paying the additional late charges. However, that person still is liable for the original balance due.