I played the enhanced editions on Steam which have a native Linux build. No issues.

I switched from using Lutris to using Heroic for my GoG/Epic games. Works perfectly for me. When in doubt, Heroic with the latest Proton-GE plays basically any Windows game, and for GoG it handles the native Linux download/install way more consistently than Lutris and its pile of crowdsourced scripts.

I'm sure it will depend a bit on your exact setup (video card especially, and likely display server too) but I can confirm that Baldur's Gate 2 (the only one I own on Steam) literally just worked with the built-in Proton emulation. I clicked install, then once it downloaded I clicked play and required no additional intervention.

GOG's Linux support doesn't extend much beyond providing you with the binaries that the developers supplied. You're left to figure out running the games yourself and hoping the developer didn't make too many assumptions about system libraries.

Valve provides Linux runtime environments for native Linux games to target and run in, plus tools for developers to use to build for that environment. It's not perfect but you'll generally have a much easier time with Linux native games from Steam.

I'm sympathetic to GOG's goals, but generally stick with Steam because of Valve's level of support and commitment.

If you want to keep using the GOG version, you could try running the Windows build in Heroic Games Launcher + Wine-GE or Proton-GE (they're available as runners within Heroic, it works pretty seamlessly). You'll also get Cloud Saves which GOG doesn't support for native Linux builds.

The native Linux version of Baldur's Gate II Enhanced is running fine for me from Steam (on Fedora 38 Silverblue + Steam installed as a Flatpak). It also features cloud saves (and achievements if you care about those), if you're set on playing the native build and willing to switch to Steam.

https://www.gog.com/forum/baldurs_gate_series/linux_libssl_fix

I found that link in this thread:
https://www.gog.com/forum/baldurs_gate_series/does_linux_version_of_baldurs_gate_enhanced_edition_work_out_of_the_box

It explains why it does not work and have a link to a solution (the first link I pasted)

EDIT. I tried it and it works

Havent tried Lutris but had success on some games outside of steam with bottles and the proton environment there.

This may be dumb, but if you can run a switch emulator maybe you can play the switch versions? It'd work like a compatibility layer.

I had issues with the "enhanced" GOG version. Starting it requires an ancient openssl library which is no longer available on modern platforms. If you launch the game via terminal or check the logs Lutris provides you might see an error message similar to "openssl.1.0.0....so not found". If thats the case I can dig up more specific instructions to circumvent the issue which got me into the game. Just to clarify, installation worked, it was just the game necer started or rather instantly crashed.

Dumb question, but did you download the Windows versions or the native Linux versions?

You're not totally out of options. Have you tried Heroic Launcher? I haven't really used Lutris since this thing came around, and it seems to do a similar job. But if not, there's a Humble Bundle going on right now with the Steam versions of both games included, and I can confirm that they work great via Steam.

Have you tried to add the game .exe as a non-Steam game, and using proton as a compatibility tool?

Are you trying the original or Enhanced Edition? I've had no issues playing the EE versions of Infinity Engine games on Ubuntu