Is not something that can be accumulated or subtracted from. If you install for example Ubuntu, Kubuntu, Lubuntu, Xubuntu....Somebuntu...Anybuntu. Each will get the support they offer for the time they offer for that particular version (Including Desktop Environments, Libraries and any other core part of the distribution).

So you would get 5 years for an LTS of Ubuntu/Kubuntu/Xubuntu....
And you would get the years/months set for a non LTS version.

When the time comes, the versions or distributions with less time will simply stop receiving updates. This is what is called an EOL (End of Life) Support. For example, if you had right now the following Ubuntu versions:

• Ubuntu 8.04 Server (Gnome)

  
  



• Lubuntu 10.04 Desktop (LXDE)

  
  



• Ubuntu 10.04 Server (Gnome)

  
  



• Xubuntu 11.10 Desktop (XFCE)

  
  

  

  
  

Looking at the image, when May 9th comes, all versions except Ubuntu 10.04 Server will still get updates. You will stop receiving any updates of any kind, including Desktop Environment updates. The rest will simply enter their EOL time, meaning they will not get any new updates (Except in very rare, security related cases and even then it is very rare indeed).

Now let me show you another case. You have 10.04 LTS. And you install LXDE, XFCE, Gnome, Gnome3, Gnome4, Gnome5, Unity 2010 Elite Edition, Wayland Super Mario version and any other Desktop Environment you can get your hands on for the 10.04 LTS version. When May 9th comes, they will all stop receiving upgrades. 10.04 will simply enter the EOL support. This is why, many times, Ubuntu developers recommend to upgrade, so you can get all the benefits of new kernels, new drivers, new hardware support, new fixes and technologies, etc..

Checking your edit in the question out:

If I install Ubuntu 12.04 LTS I will get:

Linux kernel + core stuff + Gnome3 + Unity => 5 years of support.

If I install Lubuntu 12.04 I will get:

Linux kernel + core stuff + LXDE => 6 months (?).

So I install Ubuntu 12.04 first, I have:

Linux kernel + core stuff + Gnome3 + Unity, then I remove Gnome and
Unity, then do an apt-get install lubuntu-desktop. So I will have

Linux kernel + core stuff + LXDE again. Now would I have 5 years
support time because I installed the Ubuntu LTS first or just 6 months
because I cannot cheat the system?

In all cases, you are still sticking with 12.04. Does not matter which Desktop Environment you use, you are still staying with 12.04, which means you will still get 5 years.

The years of support are not based on Desktop Environment in use, Specific libraries or any apps installed, they are based on the Ubuntu version and if it is Desktop or Server Edition.

If you install Ubuntu 12.04 LTS, remove Unity and install LXDE/Gnome 3/XFCE or any other, you will still get updates for other parts of the system. Not only that, but if there is any security issues related to the DE, you will get that also even if the support time is gone, as long as you stay with an LTS. The only thing you will not get is a version upgrade for them. Like going from Gnome 3.6 to 3.8.

I would also like to add that if you are going to be changing the DE, then there is less of a need to stay in an LTS. Upgrading the version every time a new comes out is the best choice for you. This way you get the latest DE, drivers, libraries and core updates. LTS are more oriented toward servers and users that do not want/like to be changing version or simply want a long support without changing their system so much (Because they want stability over customization). If you like to test out each DE, I would recommend sticking with the new version each time it comes out.