At a minimum, you’ll need a TeX distribution, a good text editor and a Lyx pdf viewer not working with graphics or PDF viewer. Linux, Mac OS X and Windows.
Mac OS-specific distribution based on TeX Live. These, however, do not necessarily include an editor. The easy way to get TeX Live is to use the package manager or portage tree coming with your operating system. Usually it comes as several packages, with some of them being essential, other optional. TeX Live packages should be around 200-300 MB. Linux distribution does not have the TeX Live packages, you should report a wish to the bug tracking system.
You may wish to install the content of TeX Live more selectively. It has an easy installer that takes care of setting up the environment and downloading core packages. This distribution has advanced features, such as automatic installation of packages, and simple interfaces to modify settings, such as default paper sizes. There is also a port of TeX Live available for Windows.
This section targets users who want fine-grained control over their TeX distribution, like an installation with a minimum of disk space usage. Picky users may wish to have more control over their installation. Common distributions might be tedious for the user caring about disk space. 400 MB for a functional system.
TeX Live features a manual installation with a lot of possible customizations. This installer allows you to select precisely the packages you want to install. As a result, you may have everything you need for less than 100 MB. It will let you configure the distributions, install or remove extra packages and so on. You will need a Unix-based operating system for the following. It may work for Windows but the process must be quite different. You can install collections at any time.
Schemes can only be used at installation time. You can select only one scheme at a time. Open a terminal in the extracted folder and log in as root. All administration operations for TeX Live should be made with a 022 umask. Otherwise you will not be able to use TeX at all with an unprivileged user. You may want to change the directory options.
For example you may want to hide your personal macro folder which is located at TEXMFHOME. Otherwise it allows the TeX engines to call any external program. You may still configure the list afterwards. If this option is set, format files are created for system-wide use by the installer. Otherwise they will be created automatically when needed. In the latter case format files are stored in user’s directory trees and in some cases have to be re-created when new packages are installed. Turn it off if you want to save space.