The normal way is through ceremony, in which the scroll containing the spirit of Lan's avatar (eg. the Lightning-Lord) is passed down to the inheritor of the Arbiter-General's throne and thus the inheritor of Lan's authority. As the Arbiter-Generals are effectively the spokespersons of the Hunt, this method is seen as Lan's approval, though whether or not THEY are actually directly involved in the decision is unknown.

The second, and unfortunately more common way, comes with the death of the current Arbiter-General, more often than not killed in battle. In this case, Lan THEMself will bestow the spirit onto a successor of THEIR choosing, though if the late Arbiter-General had a successor in mind, the candidate will typically align with that person.