The facility is correct and the protocol they cited is real. Correctional facilities operate largely without accountability to outside parties, and when a disciplinary situation is underway they have no obligation to discuss it with anyone on the outside, including family members and partners. The lieutenant declining to speak with you about it is standard procedure, not a personal decision.
Here is what is actually happening on your person's end. When an inmate is placed in the hole following a fight, they go through the facility's internal disciplinary process. The Disciplinary Hearing Officer, known as the DHO, handles the case. That officer functions as the judge, the jury, and the authority who renders the decision. Your inmate will have an opportunity to present their account of what happened, and the DHO will weigh that against the incident report and any other evidence before issuing a ruling and a sanction.
The entire process happens internally. You are not a party to it, you have no standing in the hearing, and the facility is under no obligation to inform you of the outcome. The only way you are going to find out what happened, what was decided, and what the sanctions are is from your inmate directly.
Mail still reaches inmates in the hole even when phone access is severely restricted, which is often the case during and after a disciplinary situation. Writing a letter now keeps the connection open and gives your person a way to communicate back when they are able. Once they can make their weekly call from the hole or are released back into general population, they can fill you in on everything.
The facility not talking to you is not them hiding something. It is just how it works.