So you need to split your water line to go to two sides of your lathe but you're not sure how.

Nothing could be easier. With the Loc-Line threaded connector, just screw this into your 1/4" NPT line, then connect a Loc-Line Y-fitting to the connector. From there you have two separate lines you can run with Loc-Line. You can add a valve to each side of the Y-connector and as much hose as you need. 

Easy.