From MEPIS Documentation Wiki
From the website: "The "Lightweight X11 Desktop Environment" is an extremely fast-performing and energy-saving desktop environment...It is especially designed for cloud computers with low hardware specifications, such as, netbooks, mobile devices (e.g. MIDs) or older computers."
LXDE is available from the repositories and can be installed in the usual manner.
Once installed, you will be able to boot into LXDE when logging in by selecting it on the pull-down menu under Session.
Tips and tricks
There is an excellent discussion of tips and tricks on the Arch Linux Wiki page.