What can be done about a employer who lies to unemployment about terminating me accusing me of drinking on the job and being under the influnence of

In Florida, a lawsuit for defamation requires several elements of proof.  It will be essential that you can prove that your employer knew or should have known that the statements were false.  You will also have to show actual damages (for example, the money you will be repaying unemployment).  There is a defense based on a litigation privilege, meaning statement made during the course of litigation are privileged and will not constitute the basis of an action for defamation.   You will need to review the facts with an attorney experienced in these types of cases.