Right now there's no way to control how a player's avatar is lit by light probes from within a world. The avatar always samples probes based on its actual world position, and world creators have no way to influence that.
In Unity this is solved by setting the Anchor Override on a MeshRenderer to a Transform positioned inside the desired probe cluster. It works perfectly on regular world objects, but VRChat doesn't let Udon touch avatar renderers, so there's no equivalent for players.
A single new API call would solve this cleanly:
localPlayer.SetLightProbeAnchor(Transform t)
This would force the local player's avatar to sample light probes from the given Transform's position rather than their actual position. It only affects the local client, is completely non-destructive.
In plain Unity this is already solved with GetComponentsInChildren<MeshRenderer>() to grab all renderers on a character, then setting lightProbeAnchor on each one. This works on any GameObject without restriction. In VRChat the only barrier is that Udon cannot call GetComponentsInChildren on another player's avatar GameObject.