Lubuntu vs. lubuntu-desktop
Solution 1:
The main difference is in the desktop environment (DE) and not in the installed applications.
(The main applications like Libre office suite and Firefox and Chromium internet browsers act ok in LXDE on computers that otherwise cannot cope with Ubuntu/Unity).
People say 'Ubuntu' to refer to the main Ubuntu release which uses Unity as DE.
Ubuntu-proper = Ubuntu OS + Gnome/Unity DE
Kubuntu = Ubuntu OS + KDE
Xubuntu = Ubuntu OS + Xfce DE
Lubuntu = Ubuntu OS + LXDE
(More here.)
The difference in resources used by Unity compared to LXDE is huge (from the point of view of my 1GB RAM PC).
LXDE/Lubuntu is the lightest, but it takes some more customization to make it look stylish (like this). (It's easy in fact.)
Xfce/Xubuntu is a bit heavier, but still light, KDE/Kubuntu is close to Gnome/Unity in the use of resources, the later being the heaviest.
For example I have a computer that is sluggish in KDE and Unity but works ok in Xfce/Xubuntu and is perfect in LXDE/Lubuntu.
You can install all the different DE that make up the Ubuntu family, try them, and then stuck to the one that best meets your needs and your computer's specs, but having them together is not very useful on the long run.
I have used Lubuntu on top of Xubuntu with no problems and do not think would be any problem to put it on top of Ubuntu-proper. In fact, a fresh install of Lubuntu would mean less stuff installed initially, that you could add afterwards anyway (like Libre Office for example). It all depends on your needs.
Solution 2:
Exactly.
Lubuntu is essentially Ubuntu, but with a different window manager / graphical shell (LXDE) and a different selection of default applications. For example, the default word processing tool is the lightweight, but powerful abiword rather than LibreOffice Writer, gnumeric instead of LibreOffice Calc, audacious for playing music etc.
You can achieve most of that just by changing the selection of installed software and selecting a session type from the login screen, but installing lubuntu-desktop will simplify this task. Moreover, as far as I understand it, installing lubuntu-desktop will not break your regular Ubuntu installation, you will be able to either use your regular Ubuntu desktop as well or remove lubuntu completely.