I wouldn't be so quick to completely tear it down.... getting the spindle reinstalled and correctly shimmed can be a PITA. There's also lots of taper pins here and there that can be troublesome.
After a good cleaning, I'd evaluate things and just take apart only what's necessary. If the spindle spins freely and quietly, I'd just flush out the oilers with some brake clean and re-lubricate with some decent spindle oil. If you carefully flip the lathe upside down, you can get to the innards of the apron and gearbox. If it's all in operating condition, clean and re-lube.