Old luggage locks like this are usually "warded locks", a very simple design with very little security.  They can be opened with a pretty simple tool which you can probably make out of junk if you need to, or you can obtain a set of warded lock-picks [on Amazon][1] for very little outlay.  (Other sources are doubtless available.)

Here's a [demonstration][2] by a well-known Youtube lockpicker.

Newer luggage locks are often of a type that can be opened with a TSA key, recognisable through a red diamond-shaped logo and a TSA00X code printed next to the keyhole.  Complete sets of TSA keys are also readily available by mail-order.  These locks are usually also quite easy to pick using raking tools.


  [1]: https://www.amazon.co.uk/WP-10-SouthOrd-Warded-Pick-Set/dp/B006JCL25A/ref=sr_1_3?keywords=warded%20lock%20picks&qid=1572733452&sr=8-3
  [2]: https://www.youtube.com/watch?v=z9UIDzwBSeI