The ABA Standing Committee on Ethics and Professional Responsibility has issued ABA Formal Ethics Opinion 519 - Disclosure of Information Relating to the Representation in a Motion to Withdraw From a Representation. The abstract reads as follows:
When moving to withdraw from a representation, a lawyer’s disclosure to the tribunal is limited by the duty of confidentiality established by Rule 1.6(a) of the ABA Model Rules of Professional Conduct. Unless an explicit exception to the duty of confidentiality applies or the client provides informed consent, the lawyer may not reveal “information relating to the representation” in support of a withdrawal motion. Disclosure of information relating to the representation is not “impliedly authorized in order to carry out the representation” under Rule 1.6(a) or otherwise impliedly authorized even when Rule 1.16(a) requires the lawyer to seek to withdraw. If disclosure is permitted by an exception to the duty of confidentiality, such as when disclosure is required by a court order, it must be strictly limited to the extent reasonably necessary and, whenever possible, made through measures that protect confidentiality such as by making submissions in camera or under seal.
You can access the text of the opinion here.