There are law review articles and other literature on this out there. There is no general reason to say a lawyer can't respond to a negative review, but a lawyer clearly has to be careful not to violate the rules of professional conduct when doing so. In particular, lawyers have to be careful not to disclose confidential information when replying to a review, and since the category of confidential information is so broad, it may prove to be very difficult to reply to a review without doing so.
It can be argued that the exception to Rule 1.6 that allows attorneys to disclose confidential information to the extent necessary to respond to a claim filed against them should apply to allow attorneys to defend themselves from attacks on negative reviews, but I think that is a stretch given the current language of the rule. As explained by a recent post in Attorneys for the Profession,
Restrictions on lawyers' ability to respond to criticism do raise some troubling concerns. Negative online reviews by clients remain on the Internet indefinitely and may even dominate an attorney's search engine results for several years, available to anyone, anywhere there is Internet access with a few "clicks." So even though the New York State Bar Ethics Committee concluded in its Opinion 1032 that the exception to RPC 1.6 should not be "interpreted in a manner that could chill…discussion," the reality is that prohibiting attorneys from fully defending against such potentially ruinous online comments does just that, by allowing the disgruntled client's side of the story to go unchallenged. A strong argument can be made that the self-defense exception to Rule 1.6 that exists in every state except California should be extended to allow lawyers to go online to defend themselves to the extent reasonably necessary in order to correct false or misleading reviews without having to fear potential disciplinary consequences. But until such a change is made to a state’s RPCs, or the exception is reinterpreted, lawyers should remember that the rules currently do not permit the use of confidential information in responding [to online criticism]. . .You should read the full post here.