How can I move an arduino library into my project repo and use it from there?
What's the deal? Aren't I supposed to be able to import libraries with
  an absolute path to the library? This is literally the same file.


Yes you can use both absolute and relative paths, but "libraries/LiquidCrystal/LiquidCrystal.h" is a relative path because it doesn't start from C:\\ or / basically. Also make sure you get the LiquidCrystal.cpp file which actually contains all the functions LiquidCrystal.h specifies.


  What is the difference between #import  and #import
  "my_libraries/myfoo.h" ?


#include "my_libraries/myfoo.h" specifies that myfoo.h is in a folder my_libraries first searched for in current_folder/my_libraries/myfoo.h then quote directories and rest of the search paths later, #include &lt;foo.h&gt; specifies that foo.h is a system header, it's only searched for in search paths.

Solution here would be saying inside your sketch that it is in a subfolder, that the folder is one folder below and then two folders deeper for ex. #include "../libraries/LiquidCrystal/LiquidCrystal.h" this here assumes your sketch is in root_folder/Sketch/Sketch.ino and library in root_folder/libraries/LiquidCrystal/LiquidCrystal.h.