Hey!
Im new to lutris, but since I stumbled upon this issue and took some time to solve it, I wanted to make a post over here for a solution being offered right here instead of having to search somewhere else.
Specifically I installed pokemon firered but when launching it, it was trying to launch for a few seconds and then it would crash - only noticable by the “Stop” button turning into a “Launch” button again. There was no actual game/window that launched, just the change in the button.
Checking the logs I found this:
Started initial process 10648 from gamemoderun /home/sam/.local/share/lutris/runners/retroarch/retroarch --verbose --config=/home/sam/.local/share/lutris/runners/retroarch/retroarch.cfg --libretro=/home/sam/.local/share/lutris/runners/retroarch/cores/mgba_libretro.so /home/sam/Games/pokemon-firered-version/Pokemon - Fire Red Version (U) (V1.1).gba
Start monitoring process.
/home/sam/.local/share/lutris/runners/retroarch/retroarch: /lib/x86_64-linux-gnu/libstdc++.so.6: version `GLIBCXX_3.4.29' not found (required by /home/sam/.local/share/lutris/runners/retroarch/retroarch)
Monitored process exited.
Initial process has exited (return code: 256)
All processes have quit
Exit with return code 256
The solution I found was from here:
Since Im using Mint/Ubuntu, i solved it by using the following commands:
sudo apt-get install libstdc++6
sudo apt update
In case you use a differnt distro, I assume you know your own installation command and if not I cant help you 
Id like to hear back if this solves your issues with any other version than I had (mine was 3.4.29), since Im currently assuming this will for an version. But Id like to make sure.
Have a nice gaming time!
Sam