There are a couple different lutes you can collect in Mortal Shell (and yes, you can play them). If you’re looking for the Impervious Lute, check out the video below for a complete path on how to get it (starting from Sester Genessa).
So what’s the difference between the Simple Lute and the Impervious Lute? Well, the Impervious Lute looks a lot more metal. I don’t really know if there are any differences besides cosmetics (and maybe song library?), but it’s cool to have nonetheless (and you’ll need to max out your familiarity with it on your way to scoring the Bars Tended Trophy).
Here’s the in-game text for the Simple Lute:
And here’s the in-game text for the Impervious Lute.
Once you have a lute, play it ten times to max out your familiarity with it.
Unfortunately, having the Impervious Lute equipped does not change which lute you play in the Brigand Life ending.