Is it lawful to be terminated for legal concealed carry without posted signs on the building?

First of all, the constitutional right to bear arms does not apply to a privately owned businesses. Accordingly, they can have a no gun policy. Further, unless there exists an employment contract or union agreement to the contrary, an employer has the right to set the conditions of the workplace much as it sees fit (absent some form of legally actionable discrimination). If a worker violates company policy they can be terminated. In fact, in an "at will" work relationship, an employee can be fired for any reason or no reason at all, with or without notice.

It is 100% legal, unless you have a written employment contract preventing termination at that time or for that reason. In the absence of a written employment contract, you are an employee at will and may be terminated at any time for *any* reason whatsoever--including concealed carry. You can be terminated as an employee at will for doing things perfectly legal, since you have no right to a job. For example: you can legally have a facial tatoo or piercings, but your employer can fire you for violating what it considers acceptable professioal dress; you have a legal right to insult other people, but can be fired for insulting customers or coworkers; legally, you can make personal phone calls whenever you like, but an employer may terminate you for making them at work; etc. The 2nd Amendment right to bear arms does not apply to private businesses; they can say you can't have your gun at work.