Well - I trried that as well but I'm not clever enough to do it without dpkg-.
I used apt-get to install kernel-image-2.4.24-1-686. When you get the LILO (or GRUB) configuration screen, press ALT-F2, Enter (which will give you an linux prompt). Type 'apt-get install kernel-image-2.4.24-1-686' (or change 686 to another arch if you're using a pre-PentiumIII machine). It should download and install the kernel.
Now return to the installer by pressing ALT-F1. You should still see the LILO (or GRUB) configuration window. Press enter to accept the default (if that's ok for you, but for many people it is) and it should install LILO. You can see the progress on the screen when pressing ALT-F3.
After LILO completed you should have the option to Finish and reboot. I hope this works :)Btw, LI (and no LO) problems most often occur when you 'change' the kernel without updating LILO.
Eric