Lookup Value Options

Hi. I'm working with a dataset that isn't mine and I can't get it changed at this time. 
There are two tables that have no relationship set up but I want to do a lookup between one and the other.

I tried to create a new column using LookupValue, and it isn't working between those two tables.  It doesn't recognize the fields
Question does the relationshp have to exist in the dataset to use LookupValue
OR 
Are there any workarounds? 

I can't change the dataset at this time.