put this in grup.conf
kernel /boot/vmlinuz ro root=/dev/hdb1
assuming that hdb is the second hard disk on the system.
Actually if suse and slackware are one the same disk check the suse configuration.
DO you have any cd burners?
If yes since slack by default uses the the 2.4 kernel, in order to burn CD's with Slack, you need to emulate your CD drives as scsi.
SO, assuming hdc and hdd are the CD roms you need something like this in the kernel line:
kernel /boot/vmlinuz ro root=/dev/hdb1 hdc=ide-scsi hdd=ide-scsi
You won't need lilo at all. Grub can boot slack.