From what little information is given, I would suspect the parting tools which you are trying to make-- on a lathe(grrrh!) are incorrectly formed and that the better choice of lubricant might- be lard oil. That is traditional stuff.
Flying in the face of those who know better- or who believe that they are, I would suggest that you get a copy of George Thomas's Model Engineer's Workshop Manual and make the rear parting tool which inverts the parting tool and projects it at an angle - downwards, has a vee of 140 degrees along the top( which is underneath really) and sufficient clearance is given to the flanks of the tool not to bind( and break).
The design of the suggested tool allows a continuous ribbon of swarf to be narrowed and then fall out of the way.
Hemmingwaykits in the UK actually sells a couple of kits designed for two sizes of lathe.
Believe me, Thomas thought it out carefully and developed the device from yet another expert's thoughts i.e Ian Bradley, author of many books and part of the Duplex team with Dr N.F. Hallows.
Of course, there are other ways and as you have found out, decent blades are expensive to replace. You pay 30 quid or so for the book, make it, learn a helluva lot and forget it. My parting tool and its holder have been on many lathes - for the last 40 or so years.
Maybe, you could try to make up a decent tool and cutter grinder. I might have helped Noah to build the Ark- but I still use a grinder.
Hope this helps you
Norm
PS
Just a thought or two. The inverted system of cutting actually can compensate for a worn or badly adjusted lathe.
N