Nope. Apple made the limit of the G4 at 10.5.8.
And that's only if you 867 Mhz or 1 Ghz or higher.
Under that, and you are stuck at 10.4.11.
To get to 10.5.8, you also need to give up Classic:
To elaborate on what a brody said:
It's not so much of a "limitation imposed by Apple" it's an actual system incompatibility. Your PowerBook is a PowerPC-based machine, opposed to current machines, which run on Intel-based hardware. OS X 10.4 and 10.5 were the two releases available during the transistion period and supported both architectures. Older versions will not run on Intel machines and 10.6 and 10.7 no longer support PPC. In 10.7, they even dropped Rosetta, a software that allowed software written for PPC architecture to run on an Intel Mac.
So yes, depending on hat machine you have 10.5.8 is as far as you can go and software development for the older OS X versions and ESPECIALLY for PPC architecture is in steep decline. I have two of those machines at home.
And if 10.7.2 was because of iCloud, you can only get limited features of iCloud under 10.5.8. Windows emulation software for 10.5.8 PowerPC is hard to come by because of most of the developers have already discontinued their product for it. You should seriously consider getting an Intel Core2Duo (not CoreDuo, not CoreSolo as neither can go past 10.6.8) MacBook or MacBook Pro, if your desire is to have iCloud. And get it up to 10.7.3, as there are security issues with 10.7.2. Sell the Powerbook to someone who needs it for Mac OS 9, or older versions of Mac OS X than 10.6. That way you won't be at a double loss for money. See my FAQ* on selling Macs.
Mac OS X 10.5 Leopard installation system requirements
Leopard is no longer available at the Apple Store but may be available by calling Apple Phone Sales @ 1-800-MY-APPLE (1-800-692-7753).
If you can't obtain a retail install DVD from Apple, look on eBay or Google the installer part numbers to possibly find at an on-line store. Here's what to look for:
MB427Z/A Leopard 10.5.1 install DVD
MB576Z/A Leopard 10.5.4 install DVD
MB021Z/A Leopard 10.5.6 install DVD (single user)
MB022Z/A Leopard 10.5.6 install DVD (5-user family pack)
Installing Mac OS X 10.5 Leopard
Mac OS X 10.5 Leopard Installation and Setup Guide
After you install the base 10.5, download & install the 10.5.8 combo update at http://support.apple.com/downloads/Mac_OS_X_10_5_8_Combo_Update
The DVD should look like this
Caution - Leopard does not support classic mode. So, if you currently open OS 9 apps in classic mode, you won't be able to do this if you upgrade to Leopard.