This is the Mac I own:

Model Name: Mac Pro v. 10.4.11
Processor Name: Dual-Core Intel Xeon
Processor Speed: 2.66 GHz
Number Of Processors: 2
Total Number Of Cores: 4
L2 Cache (per processor): 4 MB
Memory: 4 GB
Bus Speed: 1.33 GHz
OSX Tiger

What I want to do is to upgrade to the Lion OS that is about to come out. A friend told me that first I need to get the Leopard OS, then update to the Snow Leopard OS and finally buy the Lion OS.
Is that true? Is it possible to skip from tiger to Snow Leopard or to Lion in order to save some money?
Please help.

Why haven't you already tried it? Do you have an OS 10.6 DVD? Put it in and try it.

For ANY AND ALL UPGRADES on any computer (Mac, PC, whatever), you ALWAYS backup your valuable documents before getting started. That is not a point to discuss or argue about.

Yes, you can save money, but you can't also save Tiger. OS 10.6 Install DVD has a simplified installer compared with OS 10.5 and before. It cannot change any of the system files of OS 10.4.11 and before. It can change the system files of OS 10.5.x.

You can install OS 10.6 on an empty drive. As a matter of fact, the one big deal about the Snow Leopard installer is that it recognizes a Tiger system and will refuse to install over it. That's why people think it requires Leopard. It doesn't require Leopard. It requires an absence of Tiger. Those who claim they "installed Snow Leopard over Tiger" have to finally admit that they did this by removing Tiger. Well, duh! That isn't exactly "over", now is it?

With Tiger on the computer now, you will have four choices:
[1] Install Leopard (OS 10.5.x) over Tiger, which makes Tiger become Leopard.
[2] Erase the entire hard drive (you can do this by clicking the "Utilities..." button in the installer screen).
[3] Create a new partition to install Snow Leopard separate from Tiger. This has the advantage of allowing you to boot to your old Tiger system to use older software. To do this, you have to either boot to target disk mode and connect your Mac to another Firewire Mac that is running OS 10.5.x or 10.6.x, or boot to an OS 10.5.x or 10.6.x Install DVD.
[4] (if your Mac has Firewire and you have enough available space on the hard drive) you can make a folder called "Previous systems", boot to target disk mode, connect your Mac to another Firewire Mac, move the Tiger folders (Applications, Library, System, and Users) into the "Previous Systems" folder, and then boot to the Snow Leopard DVD to install normally. With a non-Firewire Mac, you could do this in single user mode (UNIX command line), but it's not for the faint of heart or those with bad typing skills, as you can mess things up by typing incorrectly.

Officially you are supposed to have Leopard before you run Snow Leopard.
Unofficially, the SL installer proceeds to install no matter what OS version you had before.