Getting started with Corona SDK
This post has links and references for getting started with Corona SDK on a Mac, and running your apps on an iOS device.
You can write your own app in Lua, or execute sample applications using Corona Simulator application. Corona SDK has several libraries at your disposal. I am particularly interested in UI development, and bridging Lua and C to access external hardware such as Bluetooth LE peripherals. That ability to build native extensions requires a paid enterprise license.
You can build and deploy the app to an iOS device for further testing. The build process happens online and requires an internet connection.