Overview page: https://www.gog.com/en/anniversary
Direct sign up for Galaxy Linux beta: https://www.smartsurvey.co.uk/t/YEF5EV/
You don't have to set up anything yourself in Lutris for games from GOG - you just go to the GOG view in Lutris where it lists all your games in GOG and click "Install" on the game you want to install and play: Lutris has scripts for the vast majority of GOG games that will automatically do whatever tweaks are needed to be done to Wine to run it so you don't have to do anything beyond that.
It's about as likely that you have to do anything further than clicking "Install" to get a GOG Windows game to run from Lutris as it is likely that you have to do anything beyond clicking "Install" to get a Steam Windows game to run from Steam, and even if you do get an issue, like with Steam in Lutris most of the problems are solved by just switching in a pull-down box in the config for that game to get it to use the latest Wine or Proton version.
As I said, I get no more hassle with running GOG Windows games in Linux with Lutris than I have running Steam Windows games in Linux with Steam.
If you run pirate games from Lutris, THEN you do often have to set it up yourself since Lutris doesn't have install scripts for such versions of the game at which point one does indeed need to dive into logs and poke around Winetricks to get the game to run (though you might get lucky, especially with DODI repacks).
Even if installing and launching GOG games from Lutris wasn't that convenient, you would be paying GOG rather pirating the game to pay the makers of the game for having made something you enjoy, and in fact I would recommend you to buy the game directly from the makers if you can bypassing the games stores (ANY games stores, GOG included) so that they get the maximum amount possible as they're the ones doing most of the work and the games stores are just middlemen taking advantage of market inefficiencies and networking effects in games distribution to get a disproportionate cut of the money for doing a tiny fraction of the work.
As a question of principle I actually chose to pay for games in GOG when I could just download pirated copies of the GOG offline installers for those games and install them just as easily - the Lutris scripts for the GOG versions of the game work for both direct download from GOG and for local offline installer files, and those local offline installer files can just as easily be pirated copies as they can be something you downloaded from GOG.