subjunctive
coniunctivus
In the prayers it is the mood of wish and petition: “may it be”. Where English says “may…” or “that Thou not…”, Latin uses the subjunctive — with it the prayer asks rather than commands.
in the texts
hallowed be — a wish-petition.
may it come.
may it be done.
with “ne” — a negative petition: that Thou not lead.