I'm running Lubuntu 12.04 on an original EeePC. In Arch Linux there's a repository which provides a highly customized very light-weight kernel specifically tailored for that particular machine's hardware.
Is there anything which would prevent me from using that kernel with Lubuntu? I understand that I'll have to download it manually and configure GRUB myself.
In general, the answer is "yes". You can always install an alternative kernel without breaking anything in your system. And since you can have multiple kernel alternatives that can be selected at boot time, you don't risk much: if your new kernel is not really working well with Ubuntu, you can always boot the system using the previous kernel.
However, the particular repository and package you mention are tailored to be used with the Archlinux distro. What that means is that while you can most likely use the tailored kernel with your Ubuntu system, you will run into problems when trying to install this kernel as a package, because Archlinux uses a different packaging system. I would not try to install that particular kernel package without understanding pacman.
Probably the best solution would then be to use the git archive (mentioned at the kernel-eee Archlinux page) to copy the package sources to your computer, and then compile and install the kernel manually. This is actually easier than it sounds, but nonetheless requires some skill and reading. Nothing for you if you just "want it to work".
Alternatively, google for "eeepc kernel Ubuntu", maybe there are packages already compiled for Ubuntu.
