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.