Ubuntu has LTS and normal version now. Does Lubuntu have the same?

No, but also yes. You will receive 5 years support on packages Ubuntu provides support for this term.

Lubuntu shares packages with Ubuntu in a sense that "underlying" "base" software like Alsa, the kernel, common shared libraries and such are from the same archive and maintained by the same people. Lubuntu is nothing more than Ubuntu with another set of preselected set of packages. It's just that Unity comes with 5 years of support and LXDE doesn't, in Ubuntu.

For the example of the kernel, Unity and LXDE core, run this on Lubuntu 12.04 or Ubuntu 12.04 (won't make a difference):

$ apt-cache show linux-image-generic | grep ^Supported
Supported: 5y

$ apt-cache show unity | grep ^Supported
Supported: 5y

$ apt-cache show lxde-core | grep ^Supported
<no output>

This way, you can check for every package whether it comes with the 5 years of support or not.

So, this makes me disagree with the other answer stating

Also, please note that if you are using Lubuntu, instead of Ubuntu, you will not receive LTS since Lubuntu 12.04 isn't an LTS release.

Because, regardless of how you installed Lubuntu¹, you will receive updates for 5 years, yet not for all of your packages (including LXDE).

¹_{You can install Lubuntu in two ways. 1) Install regular Ubuntu first, replacing Unity with LXDE via the lubuntu-desktop^ apt-task and selecting it in your login screen as desktop environment to log in to, or 2) using the Lubunu Live CD/installer directly.}

Yes. You will still receive security updates for your Ubuntu machine if you are using Long Term Support (LTS). However, not all applications will receive security updates since the LTS designation only applies to certain parts of the Ubuntu Archive.

Also, please note that if you are using Lubuntu, instead of Ubuntu, you will not receive LTS since Lubuntu 12.04 isn't an LTS release.

Examples of applications that may receive security updates are those which are supported by the Ubuntu Team or Canonical such as Ubuntu One or Firefox.

Source: An explanation of LTS in the Ubuntu Wiki

No.

Unlike Ubuntu, Lubuntu 12.04 is not a LTS, this version will be supported for 18 months. However, a lot of work has been done to improve the stability of the system.

Source

Note: Lubuntu 12.04 is not LTS, but it's based on Ubuntu 12.04 LTS. So it's very stable, the same way as Ubuntu 12.04 LTS. I'd like to recommend to you to upgrade your system to Lubuntu 12.10.

You can check the differences of Lubuntu 12.10 to Lubuntu 12.04 at this link.