Does LabTutor support the redirection of any http requests to https?

Yes, this can be achieved, but is not supported. If you run into problems our first recommendation will be to undo these changes:
To do this update the web.xml configuration file in Tomcat home directory.
1. Stop the Labtutor Service. A shortcut to the ADInstruments LabTutor Server service controller is installed with LabTutor Server and is accessible from the Windows Start menu. In the Start menu, choose All Programs > ADInstruments > LabTutor Server > Service Controller (right-click) > Run as administrator.
2. Edit the web.xml file. Locate the file in the Tomcat home directory and add the following content into the end before the closing </web-app> markup:
<web-resource-name>Protected Context</web-resource-name>
<!-- auth-constraint goes here if you require authentication -->
3. Restart the service after making these changes.