Game mods

Lua's highly flexible and easy-to-embed nature makes it appealing not only for game engines, but games as well. Several games provide a very large, comprehensive Lua API with the intention of allowing hobbyists to modify and extend the base game. Often these mods lack official documentation, but they tend to have a large active community to make up for it.

Roblox

Roblox is not exactly a game; it's a platform for building games. However, Roblox resembles a game more than an engine, which is why it's listed as a game. Roblox allows users to create and share games using Roblox Studio. It exposes programming through Lua, which exposes an object-oriented Lua API.

You can get started with Roblox development at http://robloxdev.com/learn-roblox/coding-scripts.

Garry's Mod

Garry's Mod is a physics sandbox game which started out as a mod for Half Life 2. In the version 9 release, Lua scripting was added. Players can script weapons, vehicles, entities, NPCs, and much more using Lua. Scripted...