Some of it, yes. Lubricating rollers and hinges, tightening loose hardware, clearing track debris - all fine for a homeowner with basic tools. On a door built in 1957, that maintenance matters more than on a newer one, because worn parts compound faster on older tracks.
Springs are a different story. A torsion spring under tension can break a wrist or worse if you don't know how to wind it down safely, and extension springs on older doors sometimes lack the safety cables that current code requires. If your door still has exposed extension springs with no containment cable running through them, that's worth having a tech look at even before anything breaks - it's a known gap in older setups.
If you're not sure whether your garage has torsion or extension springs, or whether your opener's reversing safety feature still works, those are both things to have checked by someone who does this for a living rather than guessed at.