For 11.10 and 12.04

For 11.10 and 12.04, you'll need to do this through a terminal.

Open up a terminal (Super, then type Terminal into the dash), then run the following:

sudo apt-get update && sudo apt-get install lubuntu-desktop

Or install via the Software Center:

You will get asked to enter your password, and you will also be asked to choose between LightDM and LXDM - I suggest using LightDM.

Once that is done, log out, and then select Lubuntu as your desktop session:

Back up your data from both operating systems.
Make a live USB or CD of the desired version the same way you did before.
Boot from it.
Then choose to install and during the procedure select install alongside and, when prompted, allow the installation procedure to overwrite the current Ubuntu installation. At your discretion, you may choose to retain the /home folder or wipe that as well. That's all.