As noted in the welcome tutorial Lua is plain text - so you can edit it in notepad. But you'll probably find you want something a bit better.
The editor you use is a personal preference - so it's up to you to choose one for yourself. The editors below are listed because they're the most popular editors in the Garry's Mod community.
A text editor with a number of features. Like Sublime Text, it also has syntax highlighting, a minimap and a number of hotkeys and a Garry's Mod specific Syntax Highlighter which can be found here.
A very good text editor in terms of looks and effectiveness, it's highly customizable and easy to use. Has a number of features to aid in development, such as syntax highlighting, a minimap and a number of hotkeys. It also has a great package manager for installing plugins. The following are a few recommended packages to install:
If you use Visual Studio then it might be more comfortable using it to edit Lua too. The free versions of Visual Studio are called 'Express'. There's a good page about Lua plugins on the World Of Warcraft Wiki.
If you're a Java developer, then you've probably heard of IntelliJ. IntelliJ is an opensource(ish) IDE for Java and many other languages including Lua. You can get the community edition for free or purchase the ultimate edition for as low as $99.
Eclipse is an IDE primarily focused on Java. If you've ever messed around with Android or Java in general, then you're probably familiar with it. Eclipse has additional support for many languages including Lua via optional plugins such as LDT.