Digging into the code I finally found what's causing this. And yes, it's related to LiteSpeed. It turns out that LiteSpeed is 100% compatible with Apache (uses htaccess, etc.), but the code that detects compatibility looks specifically for 'apache' as the server name.
IN version 0.9.2.3, replace the line 440 in w3-total-cache/inc/define.php:
return (isset($_SERVER['SERVER_SOFTWARE']) && stristr($_SERVER['SERVER_SOFTWARE'], 'apache') !== false);
with
return (isset($_SERVER['SERVER_SOFTWARE']) && (stristr($_SERVER['SERVER_SOFTWARE'], 'apache') || stristr($_SERVER['SERVER_SOFTWARE'], 'LiteSpeed')) !== false);
Hope this helps someone!
(I'll try to contact Frederick directly regarding this issue in case he's not listening to this thread)