Building your own LFS will teach you how a Linux system works internally. And most importantly, how to customize it to your own tastes and needs.
A by-the-book LFS system is fairly minimal, but is designed to provide a strong base on which you can add any packages you want.
It's not hard to get an LFS system installed under 100 MB. A few of the LFS team members have been working on creating a very small embedded LFS system. They installed a system that was just enough to run the Apache web server; total disk space usage was approximately 8 MB. With further stripping, that can be brought down to 5 MB or less.
LFS is an extremely flexible skeleton. You have the ability to turn it into whatever type of system you need it to be, customized completely for you.
An LFS system offers you added security. You will compile the entire system from source, thus allowing you to audit everything, if you wish to do so, and apply all the security patches you want or need to apply. You don't have to wait for someone else to provide a new binary package that (hopefully) fixes a security hole.
The LFS live CD is geared specifically toward providing a reliable host system for the purpose of building Linux From Scratch. Therefore, it may not be what you would envision as a "perfect"Linux system. It should, however, provide you with a comfortable enough environment so that you can, in turn, build your own "perfect"system.
To build LFS, you need to have a host Linux system with development tools. In this case, the live CD is the host system. This allows you to build LFS onto a completely blank machine.
At times, Linux distributions are built in such a way that make it difficult to successfully build LFS using that distribution as a host. Their releases may even contain bugs that are really only exposed with heavy compiling, as is done when building LFS. The live CD has been tested thoroughly and is known to successfully build the current version of LFS without deviation.
Having a live CD close at hand can be a life saver if your system breaks or suddenly refuses to boot. You can boot the CD, fix the error on your local system, reboot, and voila!
Finally, the LFS live CD includes all sources and the LFS book. This spares you from having to download all the packages individually, which can be quite time consuming. It also removes the need for a working internet connection.