There's no such thing as an obsolete Fanuc. You will have issues with old encoders, old CRT's, electrolytic capacitors in power supplies.
Not really a big deal with some basic tools and google. The worst I had was a tool magazine encoder death on a 1982 Mori VMC. I reverse engineered the encoder from the glass inside. I used the machine to make a new one using an array of microswitches running on a rotary cam plate. It took me 2 weeks to figure that one out and make the new part. I learned a lot. Learned to read and understand binary. Knowing what I know now, I'd have replaced that 1982 encoder with a $60 one from Automation direct and used an Arduino to translate the signals. I have had great success replacing obsolete encoders in other applications with modern off the shelf units. They actually make encoders that are designed to be somewhat universal so you can do this easily.
Most problems are simple. Bad LCD backlight. Weak thermal overload on a contactor. Bad servo cabling shorting out somewhere.
Learning curve isn't bad. Lathe is easy to program. I would say if you got a CNC lathe it would be best to get someone who knows what they're doing to spend a day a week showing you the basics for a month and you'd be making parts.