Could you give a quick example on how to set the esp to receive serial LUA commands from the Arduino?
You do it in the same way as you would send AT commands if you used the official AT-command firmware from Espressif.
Software:
You send the commands by serial println commands, I think using Software Serial is a good idea, in that way you can use hw serial for debug monitoring of the Arduino. http://arduino.cc/en/Reference/SoftwareSerial
Hardware:
The ESP runs on 3.3V so I strongly recommend level shifting of the Rx/Tx signals, even if I have seen reports of people getting away with direct connection. But note: 5V into the Rx pin could potentially kill your ESP.
I am successfully using this level shifting method:

Source: http://www.faludi.com/bwsn/xbee-level-shifting/
R1 can be omitted if you activate the internal pullup on the Arduino input you use for software Rx.