I assume your 1ph lathe is 240v? If so the two 1phase legs in a RPC and most Switching converters go straight through, so in theory you could use the main 240 1ph that goes into the converter, but it will pass through the PhConv O/L's. Providing the RPC is fed from sufficient gauge wiring to avoid volt drop, it should be no problem.
Make sure you fuse it separately.
Al.
CNC, Mechatronics Integration and Custom Machine Design
“Logic will get you from A to B. Imagination will take you everywhere.”
Albert E.