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Someone has actually made a mod that adds the original music! Check it out here: https://drive.google.com/open?id=1Y_RY3jmlIN8vglPI54RzL9GZ9rc0ku4Q

How would I be able to get this into my game??

If you read the README file in there it tells you, I think! Basically just download and extract the LSDR_Data folder to the same place as your LSDR installation (essentially merging the folders), and then you should be able to select a different dream journal in the game's settings that will play the original music!