Should my subpanel have a neutral conductor feeding it?
Sounds like they're trying to use the earth as a neutral, which in the US is not allowed.  

If the wires are through conduit, and the conduit is large enough, you can simply pull two more conductors. 

If the wires are in a cable, or the conduit is too small. You'll want to pull a new four wire cable, or four conductors through a larger conduit.

To compensate for the voltage drop across the 225' long conductors, you're going to have to use larger conductors.  In this case, you'll want 4 AWG copper conductors.  If you're going to install a new four wire cable, you can use 4-4-4-6 type USE copper cable.