There are 2 “branches:” of Lua now for ESP8266, and both are now open source. Confusingly, both use the word Node in their name - NodeLua and NodeMcu!

As lua.org says, Lua is a powerful, fast, lightweight, embeddable scripting language. Lua combines simple procedural syntax with powerful data description constructs based on associative arrays and extensible semantics.

• Lua is small: the Lua interpreter easily fits in under 100 kilobytes including the base libraries.
• Lua is fast: independent benchmarks show that Lua is often amongst the fastest interpreted dynamic languages. The Lua interpreter has been extensively tuned for high performance.

• NodeLua - A open source firmware runs Lua code on ESP8266, written by Harold L.
• NodeLua WebIDE - A pure web-based tool works with NodeLua for Lua programming and run codes on ESP8266 over-the-air.

• NodeMcu - Initially closed but now open source firmware, provides additional features - written by Zeroday. It is under active development.