Yes, late payments affect your scores for as long as they remain on your reports (whether the account is open or closed). While the penalty is slightly reduced as the lates age, they will continue to keep your scores suppressed until they are removed completely.
You can try the Goodwill approach with the creditor and hopefully have success with the removal of the late payments.
Welcome to the forums!
@Anonymous wrote:thanks. i have some calling to do tomorrow.
Welcome! Also, FYI -- calling may not work. Front-line CSRs/Supervisors are conditioned to say no to such requests - but you can certainly try. You may need to write a letter (or locate an email address) requesting a Goodwill adjustment and send it to management/executive offices. You can learn more about Goodwills by doing a forum search using the searchbar.
And, if you're really determined: https://ficoforums.myfico.com/t5/Rebuilding-Your-Credit/The-Saturation-Technique-Best-GW-adjustment-...
Good luck!