Are the emails ending up in a "spam/junk/bulk email" folder? At either end, is there a message explaining what happened? If AOL is rejecting her emails from her site because it thinks they're spam, she should forward the explanation (with full headers) to email@example.com
and ask that LP work to get the server off the spam blacklist. Also, does AOL permit you to "whitelist" a sender (her site) which is otherwise being blacklisted? That might help in the meantime.
It frequently happens that one bad apple on a shared server will cause the entire server to be blacklisted as a spammer (by IP address), causing problems for everyone else on the server. Or, it's some dolt on the other end, who clicks the "report as spam" in order to unsubscribe from a mailing list, rather than doing it the right way.
If there's no evidence that AOL is rejecting site emails because it thinks they're spam, and emails are successfully getting out to other mail sites (gmail, hotmail, etc.), ask LP to investigate it. She might get a free email account at other places (gmail, etc.) to have as a backup in case AOL blocks her again.