This really is not an issue but it is worth mentioning. I never quite understood why LFS decided to start using the newer version of grub since it is considered alphaware even by the grub folks.

Anyway the issue with this part of the book and the revision that needs to be here is to mention that if you did not name your kernel something grub2 likes then it will fail to setup your files correctly.

This is caused by IMHO a failure by the grub people thinking grub needs to be idiot proof and that editing a text file is too hard for most people.

I myself when having to deal with grub2 have gone back to using grub and even considering using lilo. I really never enjoy software that feels it needs to fight me on my own system and grub2 just gives me that impression.

Anyway it may be worth putting a caution in either the kernel compile step or here to warn people they will have grub2 issues if they do not name there kernel something grub can find.

What's wrong with editing grub.cfg? I've never got it to create a suitable grub.cfg automatically. I write my grub.cfg by hand using example code from the intertubes. Don't be afraid of it just because it's new. Do it like the book says, use your existing grub legacy to load the new grub; that allows you to test your configuration works before you write the new grub to the MBR.
I like the new grub because it lets me use a photo for the grub screen