You are using the -huge kernel, so there is no concern about updating initrd using mkinitrd prior to running lilo.
You probably have a line in your /etc/lilo.conf
image = /boot/vmlinuz
and a symlink /boot/vmlinuz that points to your existing huge kernel.
If you have a reliable internet connection, then all you need to do is use 'slackpkg upgrade-all' and then accept the option at the end to run 'lilo' so that the bootloader image is updated. The /boot/vmlinuz symlink will be automatically updated during installation.
If you are using any software that requires kernel modules to be built, the kernel modules will need to be rebuilt after rebooting your system following the update. Examples are the nVidia proprietary graphics driver and VirtualBox.
If you have been booting directly to run level 4 for a graphical login and you need to build the graphics kernel module, when you reboot, select your Slackware install, hit TAB and then add ' 3' (NB a space then a 3) as an option. This will cause your system to boot to run level 3, so you have a command line login.
If you have an unreliable internet connection, consider downloading all the packages first prior to upgrading. There is an option in /etc/slackpkg/slackpkg.conf that can be changed from 'off' to 'on' to allow this.