While you aren't obligated to get along with all your co-workers, lying or spreading rumors about someone at work is a very serious issue. That's why it can be so traumatizing when it happens to you, as your reputation may be tarnished by any untruths spoken about you. This is considered slander, and as the Houston Chronicle explains, there are certain steps you and others can take to deal with the issue.
A workplace's environment is integral to preventing slander and malicious rumors from spreading. Management should strive to create an inclusive environment free of gossip and rumor-mongering. A manager should never participate in gossip, as this legitimizes it among other workers. Including language about slander in the employee handbook and having meetings to address the issue is also helpful.
Evidence is key in proving the matter is legitimate. With spoken words, it can be tough to compile meaningful evidence to support any claims or lawsuits you file. You can talk to any witnesses present when the slander took place and ask if they're like to provide a statement on your behalf. You might also consider confronting the person responsible for spreading lies about you. You can do so in person, but it's recommended you send an official letter as a follow-up. It's also a good idea to speak with your manager about the issue before moving forward.
As this point, your company's human resource department will step in. They should take the time to interview you as well as the other involved party. No matter what, you want to act in a timely manner. There is a statute of limitation on slander suits, which range from one to two years in many states. If you don't file your complaint within the allotted time period, your case won't be heard by the court.