What is the difference between Lubuntu and LXDE?

Solution 1:

LXDE is a Desktop Environment, in other words, a collection of specific programs and tools like OpenBox window manager, Pcmanfm file browser, lxpanel, etc. You can have it anywhere (in fact, you actually do), for example, on Debian, Suse, Fedora, PCLinux, etc.

Lubuntu is a distro, in other words, a *buntu base with LXDE on top, instead of Gnome, Unity and other stuff specific to Ubuntu. (Note, LXDE on Debian is not Lubuntu).

Since you want Lubuntu installed, there is no reason to install Ubuntu first. Download an ISO of Lubuntu, make a CD/USB, run in Live mode, and if you like it, proceed installing.

Solution 2:

LXDE comes only with the essential packages needed to run that desktop environment. And even then there are still packages that are duplicates of their stock Unity counterparts.

Lubuntu on the other hand is a full-blown distribution with its own selection of default programs for different use cases. If you install this on a machine that's already running Ubuntu, you will be left with a whole lot more duplicate applications. On the flip-side, the user experience on Lubuntu will probably feel more coherent than on bare LXDE.

Your choice.