It's unlikely that a lawyer will be able to help with this issue. While you can file disputes with the credit reporting agencies, the fact is that the payments were made late. If your name is on the loan, the report is accurate, and it's unlikely that the credit reporting agencies will alter the score.
Your only hope would seem to be to persuade your lender to change the way it reports the late payments. However, this is something they are under no obligation to do, and they may not be willing.