Frameworks

LÖVE

This is the Lua based framework that works on desktops. There are ports that attempt creating apps for mobile device.
URL : http://www.love2d.org
Price : FREE (Open Source)
Platform : Windows, Mac OS X, Linux
Target : Windows, Mac OS X, Linux

Codea

The only Lua based framework that runs on the iPad and allows for creation and testing all on the device.
URL : http://twolivesleft.com/Codea/
Price : $9.99
Platform : iOS (iPad only)
Target : iOS (iPad)

MoaiSDK

Known as the SDK for Professional Developers
URL: http://www.getmoai.com
Price : Free (open Source), However Moai Cloud and services cost
Platform : Windows and Mac OS X
Target : iOS, Android and Chrome (Browser)

GiderosStudio

A Lua based framework that features ActionScript like syntax and Object-Oriented. Has Plug-ins and is extensible. With HotWax (a variant of Wax) iOS development is a dream come true.
URL : http://www.giderosmobile.com
Price : Free – Community, $149 – Indie, $449 – Professional
Platform : Windows and Mac OSX
Target : iOS and Android (all that are supported by the Android SDK)

CoronaSDK

A Lua based framework from AnscaLabs, now called Corona Labs.
URL : http://www.coronalabs.com
Price : $199 Indie License, $349 Professional License
Platform : Windows and Mac OSX
Targets : iOS and Android (incl. Nook and Kindle)