Are Ubuntu and Lubuntu similar enough to use a Deja Dup of my home directory from Ubuntu 12.04 to restore it to a different distro of Ubuntu - specifically Lubuntu 12.04? As I understand it there are differences beyond just the desktop environment and default apps, but I'm not quite savvy enough to know fundamentally what they are.
If you are just backing up your home folder, you will be fine. Consider that you might have both Ubuntu and Lubuntu environments on the same machine and could switch between them.
Especially since you are considering 12.04 versions of both. I believe you will be fine.
That said, for a one-off backup for the purposes of switching Ubuntu versions, I think you have two better choices: 1) simply copy your files over to a USB drive and copy them back. 2) Use the Lubuntu installer support for keeping /home but replacing everything else (Ubuntu's installer does this, I believe Lubuntu's does as well).
I'd say it "depends". Purely data files such as documents, spreadsheets, music and video should be fine.
Where you could run into complications is
If they are tailored for Unity and they replace your current Lubuntu config files, things may not work as they should. But you mostly likely won't experience data loss.
Caveat: this just seems logical to me; I have not tried what you wish to do.
Here is a link related to the issue: What is TargetEnvironment=Unity?. At first glance it may seem unrelated but, sometimes,