Using 3.3.9-std on linux:
if one enables 'own log file' access logging for a vhost and restart said vhost, logfile gets created with root ownership. Chown the file to the LSWS user to get it working.
On a not so related note, docs/Trouble_QA.html bug section should link to this forum and not the 404 http://litespeedtech.com/bugs.html
If I remove the file, it gets created OK.. it is only when the server rehashes its configuration after a logfile config change that the wrong owner is set.
Email me your public ssh key if you still need access.