Credits to this discussion here, over at Tabletop Simulator, for inspiring this post:
https://steamproxy.net/app/286160/discussions/0/541906989393418008/

Basically a workaround to the AppData storage that Limbus Company has opted to use, which does not allow us to change the directory worth ~4GB.

I have had this running just over a week, which includes the update that happened on the 16th - the game still runs fine, so I don't think this should have too much of an issue.

HOWEVER! This workaround does require the use of Command Line, and I have only tested this on Windows 10 - you should check if the commands here can run on your version of Windows before attempting.

Update 1: I have had this for about a year now - it still works fine. Additionally added in instructions on how to use PowerShell to do the same thing.

It should have a URL something like:
C:\Users\<your username here>\AppData\LocalLow\Unity
You can probably get here quicker using %appdata%, then navigating from there.

Personally, I placed mine in my Steam Directory in the D Drive.
In your original folder, the ProjectMoon_LimbusCompany folder should be deleted after this is done.

Jot down this URL, and wrap in quotes for any folder with spaces between.
So, for me, it would be:
D:\Steam\steamapps\common\ProjectMoon_LimbusCompany
DO NOT COPY THIS DIRECTLY! MAKE SURE THIS IS WHERE YOU WANT TO STORE YOUR DATA!

I did not need Administrative Rights to run it, but you might need it - try without Admin Rights first, and if it doesn't work, retry with Admin Rights.
Note: This doesn't seem to work with PowerShell, though I'm not sure about other alternatives.
^^ Credits to Cyaminthe in the comments:
"In PowerShell, you can use
New-Item -Path original_path_here -ItemType Junction -Value target_path_here
to get the same effect as mklink /j (with the same values for original and target paths)."

You will need to run the following command:
~~~~~~~~~~~~~~~~~~~~~~~~
mklink /J C:\Users\"<Your Username Here>"\AppData\LocalLow\Unity\ProjectMoon_LimbusCompany <TARGET LOCATION HERE>
~~~~~~~~~~~~~~~~~~~~~~~~
** Formatting:
The Target Location should be wherever you moved the folder to, including the ProjectMoon_LimbusCompany folder.
Any folder with spaces in between should be enclosed in quotations. So, if your folder path is:
E:\FolderWithNoSpace\Den som Griper\ProjectMoon_LimbusCompany
Then you need to put it in the URL as
E:\FolderWithNoSpace\"Den som Griper"\ProjectMoon_LimbusCompany


Once you are done, the ProjectMoon_LimbusCompany folder should reappear in the AppData folder with a little shortcut icon in the corner.

To put it simply, it just creates a "portal" at the AppData location, to the location where you want your folder. If you open the ProjectMoon_LimbusCompany folder after you have done this, your URL in Windows Explorer should still point to the AppData location, even though the storage is now done at the new location you have specified.

Do refrain from deleting the folders afterwards though - I have not tried, and I feel like the removal of the folders might be a bit more complicated than usual.

Reversal turns out to be pretty simple - since the "portal" is just a trick to redirect the program to the new location when navigating, deleting the "portal" file is sufficient to remove the link. Once you do that you can safely move the entire LimbusCompany folder back to the location.