Q. My client has threatened me with a lawsuit and an ethics complaint unless I refund her legal fees. Should I pay her to release these claims?
A. Although a refund may reduce the chances of a lawsuit or grievance, you must be very careful about negotiating a "settlement" with your disgruntled client.
Under Rule 1.8(h), you may not settle a potential malpractice claim unless this client is advised in writing to seek independent counsel and is given a reasonable opportunity to do so. Even then, you probably can't do anything to deter the client from filing a grievance against you.
Few states have adopted rules which explicitly preclude the release of potential ethics complaints. But all states recognize the importance of maintaining the integrity of the profession through the reporting of unethical conduct. In attempting to eliminate such complaints, you will "engage in conduct that is prejudicial to the administration of justice" in violation of Rule 8.4(d). Not only is such an agreement unenforceable, it is universally regarded as unethical and may itself be a basis for sanctions.
Although you can enter into agreements which may absolve you of malpractice liability, you should never attempt to negotiate with your client directly. Without using a lawyer of your own, you expose yourself to future claims that you misled the client into an unwise settlement or acted improperly in the course of negotiations. Since the client has already threatened to sue you or to report you to the bar, the less direct contact you have with this person, the better.