Does Lycos have a webpage to log in to your account? If so they should have an automated feature to email you your password (though that may not help if you don't still have access to the email account they have for you). An email to Lycos' support may also help, though they may be slow or unresponsive under the circumstances.

If you email/PM me I can give you the info I have for your FTP site. That may aid in getting full access back.

Some FTP sites and programs support transferring files directly between sites. If either Lycos or a new web host do not support this, you would need to download everything first and then upload it to the new site. There are programs that can adjust links, etc, if required (your HTML editor probably used relative links, though, so there should not be a lot of adjusting required). If Lycos finds another company to take over webhosting fully, the transfer could be done by them directly, so you could just need to fix the odd thing (like non-relative links and any listed email address).