The validation errors mentioned above were from your homepage - index.php
Yes, your login page is index_login_form.php - but when you use the lightbox, this page gets incorporated into index.php (above the closing </body></html>). So any errors in index.php could affect the imported lightbox code (ie. index_login_form.php). The 'lightbox' code just gives the illusion of a modal dialog box/window - it's really just the same page.
Something which could affect one browser and not another is validation errors in the source.
I'm only saying validation errors could be the problem...
In stepping through the code with IE's Developer Tools, there appears to be a problem submitting the form data via the XMLHttpRequest object (the lightbox hijacks the normal form submission to submit the request via Ajax) - an exception is raised in the prototype library!? You say the form submission is definitely getting through though?