do I need a lawyer?

What do you mean by "fighting this accusation"? Has some negative employment consequence (e.g. demotion, suspension, termination, etc.) occured? If nothing has happened, there is nothing to "fight" and no need for action (i.e. no consequences to seek redress for). 
If some employment action was taken against you, then the question is, do you have an unexpired written employment contract for a specific or definite term (e.g. a one-year contract), which by its terms prevents the action taken or gives you some "due process" rights to a hearing or review of the accusation? If you do, you are entitled to whatever rights the contract gives you--and if you don't get those rights, you could sue (for "breach of contract") to enforce them.
But without a written employment contract, you are an "employee at will" and your employer can take any actions you wants against you, for whatever reason or no reason at all, even based on unproven or even incorrect accusations. An employee at will, quite simply, has no rights to or at their job.
If you do suffer some negative consequences due to a false factual allegation (it must be a false factual assertion, not an opinion; everyone is legally entitled to an opinion, and opinions are not actionable), you may be able to sue the person who made the false factual statement for defamation. If you wish to explore that option, consult with a personal injury attorney.