Do I have a case if my former employer lied about why I was terminated

No, not necessarily.  Pennyslvania is an employment at will state, meaning that in most instances employers can terminate employees for any reason or no reason at all.  They can even lie about the reason and sometimes do b/c they are trying to be kind or just don't have the intestinal fortitute to be up front with employees they let go about the reasons for the termination.