I think I might have found a clue to the issue.
In the Parent library 1 – the vlookupTHISISID column is blank.
In the Child library 2 – the vLookupParentID column is also blank.
In other working vlookup lists these should have a format like this 28:1487311669532 with the first number being the ID.
I’m not sure why this is not populating though!