A lying coworker affects your work life in various ways, from your ability to get your job done on time to your personal experience in the workplace. While you might be tempted to avoid the issue, your coworker's behavior might worsen over time if you don't address the problem as soon as possible.
Review the Situation
You'll need to thread carefully with a lying coworker. Since it's often your word against hers, your boss may view it as a "he said, she said" scenario. While you shouldn't suffer from her dishonest behavior, your next steps determine how your role in the issue appears to others. For example, if you keep running to your boss each time your coworker lies but you have no real proof, you may look as if you have a personal problem with that coworker instead of a legitimate issue. Digging around behind his back for proof gives the appearance that you have a vendetta.
You should document her lies whenever possible, but not in a way that suggests you're on a witch-hunt. For example, if she sends you an email claiming she delivered papers to you on time but you have the emailed papers showing a late delivery date, keep both emails. Spoken dishonesty is much harder to document, of course, although you may speak to coworkers who overheard the conversations to confirm your suspicions and keep a written log.
Speak to Your Coworker
Talk to your coworker in private about her lying. It's possible she'll stop once you call her out on her behavior. You must remain calm during the conversation. Defend yourself if she reacts negatively, but don't become aggressive while doing so and indicate you will report her to your boss if the behavior continues. Try to end the meeting on a positive note if it goes well. For example, mention you're hoping to build a good working relationship with her going forward.
Go to Your Boss
You may have no choice but to go to your boss if your coworker won't listen to you or accept what she's doing. Bring your proof of her lies with you, but don't offer up the evidence right away. Explain what's been happening to your boss without dragging your coworker through the mud on a personal level. Mention how her lies affect your work. For example, if she's lying about delivering part of a project you're both working on, tell your boss about the impact on your deadline. If her lies are causing the workplace to become hostile, clearly state this to your boss.
Control your reactions to the situation if your boss fails to properly address your coworker's behavior or can't rein her in. For instance, you can tell your boss she's causing you to miss deadlines, but since he's aware of the situation, you just want to let him know that you're not responsible. Inform your boss you will let him know when you need something from your coworker you can't get. However, if your coworker's lying is making your workplace hostile, you may need to go over your boss and get your human resources department involved.