Source code for built in lua functions?

Those functions are exposed through C++, some may be using the new BehaviorContext already and some probably still use the AZ_SCRIPTABLE_EBUS.... macros.

The easiest way to find those functions is to search for the relevant bus and then work your way through (though that works only partly since VisualStudio can't follow the references completely). The Project you're probably going to find the most of them in is called "LmbrCentral" inside the code solution.

See the "Programming" section here: https://gamedev.amazon.com/forums/tutorials to get an idea on how to access the code solution.

Also there is reference documentation on the functions here: http://docs.aws.amazon.com/lumberyard/latest/developerguide/lua-api.html

Take note that the class reference shows functions of the new ComponentEntity system, while the file you opened is using the old entity system inherited from CRYENGINE. Specifically it looks like some sort of AI script which are different from the regular legacy entities... it's complicated, use ComponentEntities wherever you can :)

Could you tell us which project you got that file from so people can assist better?