First of all, I love onsens SO MUCH. I'm super excited to see the one Lying builds. Also someone's going to have to write cliche onsen fanfic (and it's probably going to be me tbh).
Second of all, at the very end of the episode Lying turns into a fox. Thoughts? Theories? The kitsune theory is popular, obviously, but I wanna look at it a little more.
There are two common classifications of kitsune. The zenko (善狐?, literally good foxes) are benevolent, celestial foxes associated with the god Inari; they are sometimes simply calledInari foxes. On the other hand, the yako (野狐?, literally field foxes, also called nogitsune) tend to be mischievous or even malicious. Local traditions add further types. For example, a ninko is an invisible fox spirit that human beings can only perceive when it possesses them.
Given that Lying didn't start off as a kitsune (note: he only started undergoing transformations after he and Kirin worked together, and Lying outright blamed Kirin for the weirdness in a past episode), the ninko type of kitsune might be the most likely.
Now, that being said there's also this (also off wikipedia):
In Japanese folklore, the most common types of witch can be separated into two categories: those who employ snakes as familiars, and those who employ foxes.
The fox witch is, by far, the most commonly seen witch figure in Japan. Differing regional beliefs set those who use foxes into two separate types: the kitsune-mochi, and thetsukimono-suji. The first of these, the kitsune-mochi, is a solitary figure who gains his fox familiar by bribing it with its favourite foods. The kitsune-mochi then strikes up a deal with the fox, typically promising food and daily care in return for the fox's magical services. The fox of Japanese folklore is a powerful trickster in and of itself, imbued with powers of shape changing, possession, and illusion. These creatures can be either nefarious; disguising themselves as women in order to trap men, or they can be benign forces as in the story of "The Grateful foxes". However, once a fox enters the employ of a human it almost exclusively becomes a force of evil to be feared. A fox under the employ of a human can provide many services. The fox can turn invisible and find secrets its master desires. It can apply its many powers of illusion to trick and deceive its master's enemies. The most feared power of the kitsune-mochi is the ability to command his fox to possess other humans. This process of possession is called Kitsunetsuki.
If Lying blames Kirin for the fox stuff, wouldn't it be interesting if Kirin sent a fox spirit to spy on/possess Lying? I mean, Kirin's gone on about how much he doesn't trust Lying before. And he's been dabbling in magic he doesn't fully understand. I really like the idea that while Kirin is an explorer in this world, Lying is actually a native, which would make Mineto a native religion of the land. It then stands to reason that there would be records of yokai/Mineto related folklore and magic documented in other parts of the land. What if Kirin stumbled across some of that documentation and thought 'hey, this sounds like it could help me keep tabs on Lying'. Maybe he didn't mean for the possession thing to happen; he just wanted the fox spirit to spy for him, but the kitsune was a tricky one and used Kirin's misunderstanding of the magic as permission to go possess Lying.