You have to show us the output of
Also if you change Lilo configuration in /etc/lilo.conf you must recompile it by command
If Lilo isn't happy with the new arrangement it would then tell you why.
You could change it to Grub1 or Grub2.
The easiest is to boot up any Linux with Grub1 inside, mount the Slackware partition (assumed it is hda1), copy two files into Slackware's /boot/grub, write your own menu.lst and do a setup
Step A - put Grub1 in Slackware
boot up a Linux with Grub1, like Mepis or Puppy (The Live CD may call hda1 as sda1 and make sure you know if Slackware is in the first bootable disk in the Bios. If not then make sure the boot loader knows it.)
copy Grub1 files across
mount /dev/hda1 /mnt/hda1
cp /boot/grub/stage* /mnt/hda1/boot/grub/
if you see stage1 and stage2 inside then you are in business
Step B - Create your menu.lst
use an editor to create a file /mnt/hda1/boot/grub/menu.lst with following entries
title Slackware in hda1
kernel /boot/vmlinuz ro root=/dev/hda1
Step C - Install Grub1 in MBR
Let us know if you want Grub2 instead of Grub1.