First - you need to discuss this question with an attorney in the state where the defamation occurred. The following information is based on Texas law and may be different in other states.
Members of an LLC, in their capacity as a member, are not responsible for the conduct of other members of the LLC. It is possible for other members of the LLC to be responsible for the defamation but the liability would be based on something other than owning an interest in the LLC.
Even though the other members may not be liabile, the LLC could have liability for the defamation. Defamation is what is known as an intentional tort. If the individual that committed the defamation was acting in his capacity as an agent of the LLC, or if the LLC authorized the defamatory conduct or knew that he was engaging in defamation and did nothing to prevent or correct it, it could be held responsible for damages for the intentional actions of its agent. This is a doctrine known as Respondeat Superior and makes the principal (ie the LLC) responsible for the actions of its agent (ie the individual member). So even though the other members of the LLC may not be responsible, they may bear the cost of the defamatory conduct indirectly through their membership in the LLC.
As I said at the beginning, you should discuss this with an attorney licensed in the state in which the defamation occurred because their laws may be different. I hope this gets you headed down the right track. If you found the information useful, let me know by clicking the "thumbs up" button below.
DISCLAIMER - Mr. Wilson is licensed by the State of Texas and practices in the areas of general corporations, mergers and acquisitions, and securities regulation. He is not certified by the Texas Board of Legal Specialization because there is no certification for those areas of practice. The above information is for informational and educational purposes only and does not constitute legal advice. No attorney client relationship is created or implied by answering questions on .com.