Is anyone else having problems with Autocad?

I would check the Security & Privacy preference settings to be sure the app is not being blocked. If that fails you could try reinstalling Autocad LT? As long as it does not depend on Java there should be no issues.

Other System Requirements:

(You could send Autodesk a note about the app not launching)

http://knowledge.autodesk.com/support/autocad-lt/troubleshooting/caas/sfdcarticles/sfdcarticles/System-requirements-for-AutoCAD-for-Mac.html

You might want to check the Console logs when you launch the app to see any system messages that might help diagnose the problem a bit further.

Hope this helps.