Unable to install Internet Explorer on MAC OS X 10.7.4
There is no Internet Explorer for Mountain Lion.  

If you must have IE you need to run Windows virtually (e.g., with Bootcamp).

I would try the Chrome or Firefox (or Safari) on Mac and see if they can work for you.

In Safari, you can try this:


Go to Safari > Preferences > Advanced > click on Show Develop Menu in Menu Bar.
In Develop menu > User Agent > Internet Explorer 9.0


This might trick the websites into thinking that Safari is Internet Explorer.