Looking at the contents of the page, the inputs and some hidden values on the login form have been replaced with 'lscache'. For instance:
<input type="hidden" name="lscache_formtoken" value="1">
The form token is normally a long string of characters that's used for security purposes. If you have some sort of caching turned on that's trying to be agressive about how it caches the page, it's likely you'll need to disable or reconfigure how that works so that our login form works.
Do you know what lscache is? Can you reach out to the developers to see if they have issues or solutions for their caching to work with login forms?
I hope that helps point you in the right direction.
Thanks,
Melissa