If you told of your qualifications or experience running a lathe or machine tools in general someone might be more willing to extend you the opportunity to use their equipment.
In my early years
Since High school I've completed quite a few machining and welding classes that included training on various types of machining equipment that in itself would probably equal an associates degree if it were able to be all bundled up, and that led to working a couple years as a machine technician for Diablo valley college in CA where I was once again taking classes to finish personal projects (they even had a TIG welder!)
In Southern CA I even attended a government sponsored 8 month long machining school that included CNC programing.
That class let to a job working for a small grinding company in southern Ca for a while before I moved back up to northern CA.
More recently I have completed my Associates in applied science at Joliet Junior College for CADD, that, once again also included quite a few machining classes that I took advantage of.
The plan was to get an inexpensive lathe and mill but the 2008 crash killed that idea.
Now I'm building
1: A Romanian PSL with a custom barrel.
2: Making an accessory barrel for my H&R Handi rifle in 7.62x54R.
3: I'm rebuilding an old school Black powder 12 Gauge double barreled shot gun (A counterfeit Greener made in Belgium) with modern barrels able to handle smokeless powder shells.
4: I also have a Polish DPM gas block I need to machine the cut off barrel out of because the hardened pins will not come out!
That's about all I can think of for now as far as experience and lathe projects.