Can my former employer (atty) claim slander against me for info I had to provide to Dept of Labor investigator for unemployment?

Truth is always a defense to a claim of slander, but is often harder to prove than is first thought. Many states, like Texas, recognize a "privilege" in litigation that precludes filing a slander claim based on statements made in pleadings filed in court, whcih relate to the legal matter. Because your statements were made in the course of an official proceeding, this litigation privilege may well protect you with respect to the statements you made to the Labor Dept. This privilege only applies in official communications so dont share your letter or comments with others or the protection will not apply and you will be back to having to prove truth.

Unemployment benefits are intended for individuals who lost their jobs through no fault of their own. In some cases, even though the employee "quit" technically, the separation from employment was the the employer's fault. From the limited facts you provided, it seems that is what you are claiming.

You can't be found liable for slander unless you lied or, depending on the state ylaw of Idaho, painted the attorney "in a false light." However, you also have a duty not to reveal certain confidential information regarding your employment. In addition, you could be sued for breach of contract if you signed a non-disclosure agreement with the former employer.