Legal Question in Civil Litigation in Nevada

I am going to assume you mean that the third-party action names the plaintiff's attorney as a third-party defendant, alongside his client. That is a very unusual set of circumstances, if I have the facts right, but not unheard of.

Conflicts of interest can be resolved with the consent of the involved parties. If the attorney's client waived any dispute and consented to his/her representation, despite the peculiar juxtaposition of the defendants, it likely would be allowed by the court. If, however, their interests collide (such as if they would have claims against each other as a result of your desired outcome in the third-party action), it could be deemed entirely inappropriate for the lawyer to continue to represent a party against whom he may pursue a claim, whether for substantive relief or in indemnification and contribution.

A competent attorney would have to review your facts and the substance of the pleadings to really answer whether this presents an impermissible conflict of interests.