Like my decision to offer my platelet and plasma donations to Apollon and Asclepius, I considered my service as an offering not only to Athena, but Eunomia and Dike as well. All prospective jurors were required to swear or affirm that they would fulfill the duties required of them, including not discussing specifics of the trial that they may be impaneled for. As someone who is very much aware of the seriousness of an oath (as discussed in this link from 2012 as well as others shortly after) I took that as befitting the seriousness of the responsibility that jury duty entails.
While, ultimately, I was not selected to be on the jury, I still consider being a potential juror as something that is part of my civic responsibilities, and because it was considered a sacred duty in ancient times, I would say that this is something that remains sacred even now.