liloconfig sets up /etc/lilo.conf too, but if you have it set up the way you want then all you have to do is run "lilo." Don't forget to make sure that the /etc/lilo.conf file also has the Debian installation in there too so you can boot to that as well.
Yes it's fine to run lilo(config) from a Slackware installation. Although I can't say for sure what errors (if any) you'll run into with GRUB2. Also, make sure that the generic kernel exists in your /boot. Otherwise if there is no generic kernel, obviously you won't be able to boot the generic kernel. If it's not there, just use slackpkg to install the generic kernel.
If you don't create the initrd and run lilo, then lilo can't pick up the initrd anyways since it doesn't exist. Create the initrd first, then edit /etc/lilo.conf to pick it up and run "lilo" to apply the changes.
I also like to use "mkinitrd_command_generator.sh -i" for interactive mode (that's just a personal preference). Maybe you'll like it too? I don't know.