Your first thought might be that IE 7/8 doesn't support HTML 5. While that may be the case, there's still a very simple fix that allows you to use the HTML 5 based Facebook like button code on early IE browsers.
Simply add the following attribute to your HTML tag:
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en" xmlns:fb="http://ogp.me/ns/fb#">
This is mentioned as necessary when using XFBML to display the lightbox, but not for the HTML 5 version of the code. Eithery way, it does seem to do the trick.