That really depends on the email. AOL has a web based program, but also pop3 still, I believe. If it were Pop3 and you already downloaded the emails without keeping a copy on the server, then, yes, if you don't remember the password and cannot recover
it (which is odd), then they would be lost.
If it is a web-based email than you will be much more likely to get the emails back as they are stored on the server until you physically delete them. I would suggest googling your email program (AOL) and looking for answers that way (or calling).
I don't have enough details from you to walk you through the steps.
Hope you recover your email.