Why not use GRUB instead of LILO?
GRUB will very likely replace LILO in the book when the GRUB maintainers made a release they call stable. If you’d like to see that happen, you could bug the GRUB maintainers, since current releases seem perfectly stable. If your current setup uses GRUB or you’d like to use it anyway, you should have no trouble following the GRUB documentation and the LFS “GRUB-Howto” Hint at http://hints.linuxfromscratch.org/hints/grub-howto.txt. If you do this, you can omit bin86, since it is only used by LILO.