How do I get it to run on Linux? I have a Legion 5 RTX3070 and am struggling, any help gratefully accepted!
I assume you meant Horizon Zero Dawn.
According to WineHQ you need to install vkd3d with pacman and then install vcrun2019 with winetricks into your 64-bit wine prefix where you have the game instaled.
It can go like this (no guarantees that it will work):
# create clean 64-bit wine prefix - change the directory path as you like
WINEPREFIX=~/wine64 winecfg
# install vcrun2019
WINEPREFIX=~/wine64 winetricks -q vcrun2019
# install vkd3d
yay -Syu vkd3d
# install the game
WINEPREFIX=~/wine64 wine ~/path/to/installer.exe
# run the game
cd ~/wine64/drive_c/path/to/installed/dir
WINEPREFIX=~/wine64 wine something_something.exe
If you mess something up you can just delete the wine prefix.
rm -r ~/wine64
There is also an installer for it on Lutris
Nope, can’t get it to run, TBH giving up 
Sometimes it can take a bit of trial and error, I had trouble with a game not being able to launch the other day and it turned out to be that I didn’t have a certain 32 bit package installed on my system which I found out by running it in the terminal.
I have played HZD and finished mostly on Linux, with a 3070, with few problems (by which I mean none outside of specific nvidia driver versions)
I used the steam version with proton, but I assume you could install the GOG version as a non-steam game in steam, and get basically the same setup in 2 minutes.
I tried that, it would start to load then crash (can’t remember the error).