Will I lose a lawsuit if I can prove the person lied when they filed it?

It is not possible to answer your question from the limited information provided. The court will determine the outcome of the case from the totality of the circumstances, not necessarily from a single fact (or email). The email is one element of proof, but not the only proof, that the court will consider. For example, the other side might succeed in proving that the email is forged, that it was sent by mistake, or that, when taken in context, it means something else. Finally, the fact that the plaintiff lied about something does not mean that the plaintiff loses; that misstated fact may be immaterial, or not consequential, to the outcome of the case. Lots of considerations go into the outcome.