Ah, another game with a Linux port but not on GOG. Seems it was done by Feral Interactive and iirc. there was an issue with Feral publishing on GOG (or maybe having exclusivity deals with other trade platforms?).
Would be nice to have the Linux port here, too, though.

Unfortunately, Feral abandoned the game and it actually runs better on Linux using Proton: https://www.protondb.com/app/234140

That's if you use something like GameHub and can get it to work. I do wish we still had the native port on here.

With Feral they support DRM so no chance of there ports coming here. Some people have claimed that running the Windows version through WINE or Proton gets better performance than the Feral Linux build.

As others have pointed out: so far Feral have no plans on selling games at GOG (or anything non-Steam for that matter).

https://www.reddit.com/r/linux_gaming/comments/8axa70/rise_of_the_tomb_raider_coming_to_linux_this_month/dx2decr/?utm_source=reddit&utm_medium=web2x&context=3

Said it before, and I'll say it again: Choosing Linux over Windows comes with some sacrifices.

Well, I bought it on sale, 5 Euros seemed very affordable to try. As soon as I find the time (which can be more than a year due to my workloads), I'll check and see if I can get it to run via wine. Likely people will already have tried. And proton is basically wine as far as I see. I value Valve's engagement in Linux, but DRM frightens me.
Sad for Feral that they seem to cling to Steam only. Contracts or free will, I don't know. But I don't like buying something that is endangered to suddenly stop working because activation servers are down, the publisher doesn't like my nose or they went bankrupt.

Feral did create a Vulkan beta for Mad Max that runs about on par with Windows' DX11.

If you are playing the GOG version, try to use Lutris or Bottles and use the Wine-GE or Proton (GE or standard) if you can.