Talk to the lawyer. The NDA may have an arbitrary clause but that would be for violations of the NDA its itself. Your work would be covered under an employment contract of some sort either a implicit contract which you say you don't have or an implied contract which would be the emails that you exchanged in which describe the work that you would do and the compensation that you would receive.

This is a typical labor dispute. They probably have no money or very little funds and so they're seeking to reclaim it from you. The moment they threatened to sue is the moment you should stop talking to them and refer them to a lawyer. Everything that this hinges on is the initial emails that you exchanged which described the work, the time frame and the compensation that you would receive.