Our wiki has a good deal of information to help you with developing LGM. For starters, getting the code set up for dev initially is documented here:http://enigma-dev.org/docs/Wiki/LateralGM:Developing
Understanding the layout of the code is the next task, documented here:http://enigma-dev.org/docs/Wiki/LateralGM:Packages
All of the file-handling code is contained within /org/lateralgm/file/
All of the frame code for e.g. the frame shon for editing a Room or an Object is contained within /org/lateralgm/subfarmes/
All of our custom components, like custom widgets like the ResourceMenu and IntegerField, are in /org/lateralgm/components/
While LGM was designed to be cross-platform, and mobile devices technically support it (since it is Java), I never considered it worthwhile to do, due to the extreme limitations of mobile platforms (such as the lack of a normal keyboard or two-button mouse) which make IDEs on them less-than-trivial. So while you're welcome to do it, and I'm certainly not going to stop you, I'd just discourage it because it seems silly. Instead, you might try shifting your efforts towards getting games to compile for mobile devices (enigma-side).