Is there a way to assign lights to objects so that the light only lights up that object? I know in other 3D programs you can assign light lists to objects so only that object receives light from the lights on its light list.
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Unfortunately, light groups were removed in Blender 2.8. "Light linking" is a much requested feature but isn't currently supported in Cycles or Eevee.
Here is a video from Blender Conference 2018 with an AMA with Blender developers where they talk about this specific topic. One of the lead developers talks about how there are no "fundamental problems" including it in Blender, but that he mostly discourages its use, instead advising that users test their materials in different lighting environments to avoid having to resort to these kind of edge-cases.
Here is the current developer task about this feature where there is further discussion (and pleading).
There are some alternative ways to do this via compositing that I am looking in to, and will update this post if I find anything viable.