If you replace GRUB with LILO in Debian (or derivatives), you're likely to encounter a situation where dpkg tries to run 'upgrade-grub' as part of installing a new kernel. Unfortunately, with grub missing, this will fail making kernel installation impossible. On the bright side, the answer is simple.
If you look at your /etc/kernel-img.conf file, it should look something like this:
# Kernel image management overrides # See kernel-img.conf(5) for details do_symlinks = yes relative_links = yes do_bootloader = no do_bootfloppy = no do_initrd = yes link_in_boot = no postinst_hook = update-grub postrm_hook = update-grub
Simply change it to remove the grub hooks and make it call your default bootloader instead (e.g. LILO):
# Kernel image management overrides # See kernel-img.conf(5) for details do_symlinks = yes relative_links = yes do_bootloader = yes do_bootfloppy = no do_initrd = yes link_in_boot = no
After making the changes, dkpg should be able to install your kernel without any problems, calling LILO afterwards as prescribed.