Hello and welcome,

I think Elixir is a good fit for game server because You can isolate a game state in a process.

There are many example on the web… (some are outdated, but concept stay the same)

• Poker https://tokafish.com/playing-poker-with-elixir-part-1/
• Battleship https://github.com/bigardone/phoenix-battleship
• Tic tac toe https://alchemist.camp/episodes/tictac-game-board
• Tetris https://www.youtube.com/watch?v=z7kGWyLt1GQ

There are games in those paid resources too

• Island game Functional Web Development with Elixir, OTP, and Phoenix (Pragprog)
• Bingo Unpacked: Multi-Player Bingo (Pragmatic Studio)

But if You want to use it with Lua, maybe this

Many projects have been done because Elixir helps isolating games, and with phoenix channels, You might also reach for graphical game.

For example, combining Elixir with Three.JS, Babylon.JS, Phaser.JS, Godot, Unity3D etc.