You need to make an new initrd image for each specific kernel.
See the man page for mkinitrd.
Also you dont need to replace your old kernel, just add an entry for the new one to your lilo.conf and keep the old one around for emergencies.
When you copy the new kernel to /boot also copy the System.map file in /usr/src/linux (or whereever you compiled it) name the System.map file for the kernel version, ex for kernel 2.4.20 you would name the System.map file "System.map-2.4.20" and copy it to /boot and name the new bzImage
vmlinuz-2.4.20 and copy that to boot. Then make the appropriate lilo.conf entries and run /sbin/lilo.
You can have as many kernels as you want. Collect 'em, trade 'em, name 'em after your pets