Thanks for using Lunascape!
It would seem Internet Explorer does not handle very well some things in the game you mention, so perhaps the Trident engine in Lunascape also does not handle some things well for the same reason (it is the same engine as the one used by IE).
If I switch to Gecko however everything seems to work fine, so try using the Gecko engine in the tab where you are playing the game. To switch engine of an active tab, right-click on the tab to display the context menu and select Switch Engine - Gecko (FF).
If this does not help with your problem, try changing the media settings in Lunascape. To do this, open Lunascape Settings via the Tools menu and then select Advanced - Security. The page that opens lets you enable/disable various media, scripts etc.