Lubuntu uses LXDE for the Desktop Manager (the GUI), which supposedly runs with only 512 MB of RAM as opposed to Unity, which is a known memory hog. Thus, it would be "lighter". From the LXDE site:
Lightweight
It needs less CPU and performs extremely well with reasonable memory.
Fast
It runs well even on older computers produced in 1999, and it does not require 3D acceleration.
...
The hardware requirements of LXDE are similiar to Windows 98 (Maybe a little bit higher). An old Pentium II CPU is enough.
After X11 and LXDE are started, the total memory usage is about 45 MB on i386 machines. (This value may be higher or lower according to
different system configurations.)
Though LXDE itself doesn't require better hardware, other applications under X do need it. For example, Firefox and
OpenOffice.org 2 are quite memory-hungry. So it's recommended that you
have a RAM of more than 128 MB.
As for the applications that come default installed with Lubuntu, they are lighter and run on less RAM. They may have less features, but they are built to run on older equipment, such as my iBook G4 (downloading the iso for Lubuntu 12.04 now :D).
You can read here: https://wiki.ubuntu.com/Lubuntu#Lubuntu_vs_Ubuntu about the comparison. Basically, what makes Lubuntu lighter (faster) is the DE, LXDE.
Thus, LXDE itself runs lighter/better on older/limited hardware. You can read more about this on the LXDE about site: http://lxde.org/lxde.
As for which one to go with, I would try going with Lubuntu first and then if you want it, install Unity. I've heard (not confirmed though) that Lubuntu is faster overall and thus you can just add the apps you want after the install.
I have an old 7-8 yr old Toshiba Satellite A105 with 1GB of RAM and Unity runs, for the most part, great on that. If I have a large number of tabs open in Firefox or several apps running at once it slows down, but usually its fine!
So, it really comes down to the speed-features trade-off. Unity/Ubuntu seems to have more features, but LXDE/Lubuntu has more speed. It's really your choice.