Is it illegal to lie and say you're under an NDA?

Based on the [scant] information you provide, you are fine.

Your description nowhere reflects that you have a duty to disclose to that person (1) the information he is trying to gather from you, or (2) whether or not you made any arrangements/agreements with third parties. Accordingly, your false statement is not actionable.

By contrast, that person's retaliatory attempts to harm your reputation might render him liable for defamation and --depending on his method of defaming you-- possibly other torts.

Generally speaking, no.

Assuming your lie did not cause some "legally cognizable harm" -- as in the case of perjury, defamation, fraud -- it is almost certainly protected by the First Amendment. United States v. Alvarez, 567 U.S. 709 (2012).