Lathe drive systems vary, and hence the maintenance schedule for those will vary by machine. My previous lathe had a Reeves drive, which required belt replacement and pulley to shaft lube, but it was infrequent, check the belt 1-2 times a year. The pulley only needed lubed when it started to get a little stiff. My current Nova DVR drive is maintenance free - blow out the back of the HS occasionally.
I point this out as an example - most all aspects of lathe maintenance can be done based on “feel”, if you trust yourself. When a friction surface starts to feel tight - a TS quill, banjo feels a bit “ sticky”, etc, it is time for maintenance. Time spent on these items before they need it is unnecessary, again, provided you trust yourself to notice.
Keeping wet shavings off bare ferrous surfaces prevents rust, and you can see the tarnish immediately if not - time for maintenance. Blowing out open drive components - inverters and motors - everyday you use the machine. Drive belts - if you typically change speeds, thats inspection time. If you dont, probably inspect 4-6 months.
Cutting tools get cleaned before sharpening, and gunk gets wiped off after cutting before going in the tool holder.
Not a fan of any lube that remains wet to attract dust. Only place is the quill acme thread gets grease. All other friction surfaces get paste wax, including chucks - they are disassembled, cleaned and deburred when I get them, waxed, and usually never opened again, blown out often.