Aleaxes are rarely generated randomly and will never appear in Gehennom. They may appear as lawful minions; randomly generated Aleaxes will be peaceful towards lawful characters with good alignment record.
They are generated with a blessed erodeproof long sword and a non-cursed erodeproof large shield. There is a 1⁄20 chance that the sword will be converted into either Demonbane or Sunsword (if the chosen artifact does not exist yet), and a 1⁄4 chance the shield will instead be a shield of reflection.
In UnNetHack, an Aleax behaves more like the D&D Aleax (as described below), and will be generated wearing an erodeproof +0 copy of all of the player's equipment and weapons; artifacts will be converted to their base item.
In Dungeons & Dragons, an Aleax is an avatar of a deity sent to punish a specific mortal; the Aleax takes on the target's exact appearance and carries identical equipment.
An Aleax, according to the AD&D Fiend Folio, is a creature that
looks exactly like the character, and is sent by the character's
god to punish alignment violations. Obviously - and luckily - in
Nethack this is not the case.