Well, it wasn't a re-write rule issue and it was nothing to do with LiteSpeed. It was actually my .htaccess file, as created by Admin Tools, which was blocking user access to the download.
jDownloads is using directories outside of Joomla's standard locations for downloads. Admin Tools considers this to be "bad practice". So, if you are using an .htaccess file created by Admin Tools, it is necessary to explicitly include all jDownloads category sub-directories (this is easily done using the Admin Tools .htaccess maker tool). However, because the directory name cannot have spaces in it, this means that jDownloads category names cannot have spaces in them.
It would be great if this could be added to the documentation.