The parting tool needs to be as rigid as possible, so minimise the overhang. My HSS blade is adjusted for minimum protrusion from the holder .
If parting off large diameters, I rig a gravity feed to a home made needle valve and jet held on a small magnetic post on the Cross Slide, so that the blade gets a steady drip, or flow of soluble oil.
The feed comes from a plastic "pump" bottle on a shelf above the lathe, with the feed tube being a length of plastic screen washer pipe pushed onto the spout from the pump. The pump is handy to prime the system and start the soluble oil syphoning down the tube to the workpiece.
Howard