Currently the module allows conversion of new filenames to lower-case.
There is also an option to transliterate existing filenames, but this doesn't change their case.
I want all filenames to be lower-case so as a quick work-around I edited function transliteration_file_query in transliteration.admin.inc, changing
$operator = 'NOT REGEXP';
$operator = 'NOT REGEXP BINARY';
The problem is that by default, MySQL's "REGEXP is not case sensitive, except when used with binary strings." (see http://dev.mysql.com/doc/refman/5.1/en/regexp.html). Adding the 'BINARY' makes it case sensitive.