You can boot to your installation media, mount the root partition, chroot into it and run lilo.
Just to be complete, boot into your installation media and login as root (no passwd), then...
Code:
mount /dev/sdxy /mnt (where x is the Slackware drive and y is the root partition)
mount --bind /proc /mnt/proc *** See below ***
mount --bind /dev /mnt/dev
chroot /mnt
vi /etc/lilo.conf
...make any necessary edits for the new kernel...
lilo
Then reboot...
That should work for most cases I think.
Try it and post back if you get stuck anywhere.
**** Update ****
It has been a while since I did this - it now occurs to me that will need to bind the /dev directory at least, and maybe the /proc directory before chrooting...
So
after mount and
before chroot in the steps above add these... (I have now done this - sorry if that created any confusion for you!)
Code:
mount --bind /proc /mnt/proc
mount --bind /dev /mnt/dev
...that will assure that lilo can see the /dev/sdx partitions!