Drupal does not support lighttpd as a server for deployement. And appart form the problems you may have with .htaccess files not working, there is also another minor bug: https detection in drupal is done with the $_SERVER['HTTPS'] variable, which is not available when running PHP in CGI mode with lighttpd. The result is that you will be moved to http after logging in via https, which is not what you want. So a quick fix is in order.
Open the file includes/boostrap.inc and in the conf_init() replace the code stating:
<?php
$base_root = (isset($_SERVER['HTTPS']) && $_SERVER['HTTPS'] == 'on') ? 'https' : 'http';
?>with something that uses the $_SERVER['PORT'] variable:
<?php
$base_root = 'http';
if(isset($_SERVER['HTTPS']) && $_SERVER['HTTPS'] == 'on')
$base_root = 'https';
elseif(isset($_SERVER['SERVER_PORT']) && $_SERVER['SERVER_PORT'] == '443')
$base_root = 'https';
?>I don't think this patch will ever get into drupal, because running an HTTPS server beind any other port then the default will still fail this test, so there will have to be some other solution to fix this properly.