When a facility says an inmate is in lockdown and the email system is simultaneously blocking your messages, those two things are almost certainly connected.
There are two different kinds of lockdown worth understanding. A facility-wide lockdown affects everyone at once, usually due to an incident, a search, or a staffing situation. In that case all communication gets suspended temporarily and restores once the lockdown lifts. But when it is just your husband who cannot receive messages while everyone else is presumably unaffected, that points to something different.
If JailATM is specifically blocking your messages to him, it strongly suggests his communication privileges have been suspended individually. That happens when an inmate is placed in disciplinary segregation, which is separate from a general lockdown. In that status, email, phone, commissary, and visitation can all be restricted or eliminated entirely, depending on what the infraction was and how the facility handles it.
The jail telling you only that he is in lockdown without further explanation is frustrating but not unusual. They are not obligated to share disciplinary details with family members.
The most direct path to answers is to send a physical letter. Mail typically continues to reach inmates even during disciplinary segregation when electronic communication is cut off. InmateAid can get a letter to him without your home address on the envelope. Ask him directly in the letter what is going on and when his privileges are expected to be restored.