There are no general laws preventing employers from giving out false information (lying). However, the real issue is if the false information they gave out violates any law. While state laws vary, here are some ways giving out false information about a former employee may equal a lawsuit:

Defamation: If your former employer is giving out false factual information that damages your reputation, then you may have a claim in your state for defamation. State laws on defamation vary, but the basic elements of a defamation claim are that the former employer made a statement they knew was false to a third person (could be verbal, in an email or text, or in a letter), the statement was one of fact, as opposed to opinion (they say you stole, missed 10 days of work, or you were fired when you actually quit), and you were damaged as a result.

False light: Some states recognize a claim called false light invasion of privacy, which is similar to defamation but can apply even to truthful statements. Basically, it means the former employer maliciously made a statement about you that places you in a false light, and that the statement was highly offensive or embarrassing. An example would be if the employer says you left right after a big fraud scandal at the company, but failed to mention that your leaving had nothing to do with the scandal. Giving unbalanced performance feedback (only mentioning negatives when there are also positives in the employee record) could be another example of this.

Tortious interference: If you have a job offer or have already started working and your former employer gives out false information in order to cost you that new job, then they may be liable for tortuously interfering with your new employment. This happens more often than you'd think.

In general, if you think your former employer is giving out false information about you the key is being able to prove it. There are some professional reference checking companies you can find online that will pretend to be a potential employer and find out what they are saying about you. You'll get a report telling you what was said and by whom. In some states, this might be enough evidence. In some states, you might have to subpoena a potential employer and have them testify about what the former employer said about you. Most won't want to get involved and may even lie to protect a fellow employer.
 

Even if you decide not to sue, an effective way to stop this practice is to send a cease and desist letter to demand the former employer stop giving out false information. Once they know they're caught, most will stop. Sometimes the person giving out the false information will even be disciplined or fired.