Can I be lawfully terminated for an inappropriate facebook comment?

[Sylvia]

This is perfectly legal. Most companies and government agencies hire employees "at will". This means that they can terminate you for any reason. Your boss has reason, however, because you were on company time doing personal business (which is considered stealing) and using a company computer. I'm sure if you look up in your employee handbook, there will be something that says it's grounds for termination/suspension to steal company time and to conduct personal business while at work. They don't have to let you know that they are using a special software; most people are smart enough to know this is done.

What you did was not very smart. Many people aren't very smart when it comes to social media. Good luck in your new job search.