can a company lie about me working for their company.

A prior employer cannot provide false information about you that would be deemed defamatory.  If you worked there and they are telling others you did not, that causes you to be thought of as a liar.  You should contact the HR company first to make sure they are aware that you did in fact work for them so this does not occur again.  If the false statement caused you to lose a job or they do this again, you can consider legal action for defamation.