Rather than a make install as the last step (ive never used it but im presuming that it installs the new image as /boot/vmlinuz) you might want to copy the neccessary files to /boot and make the initrd.img by hand. This way you can preserve the old kernel image and have a way back out.
So I would recommend as the last few steps:
cp /usr/src/linux/arch/i386/boot/bzImage /boot/vmlinuz-2.4.20
cp /usr/src/System.map /boot/System.map-2.4.20
mkinitrd /boot/initrd-2.4.20.img 2.4.20
Next edit lilo.conf to add the new entry:
image=/boot/vmlinuz-2.4.20
label=2420
root=/dev/hde7
initrd=/boot/initrd-2.4.20.img
append="devfs=mount hdc=ide-scsi"
read-only
Thats my entry for 2.4.20 so you may not want the append line.
Next step:
RUN LILO !!!!
In caps with exclaimation marks because I forget sometimes
/sbin/lilo
If you dont get any errors from lilo try to boot the new kernel.
/usr/src/linux on my desktop machine is usually just a link to whatever source tree im currently playing with ... currently 2.5.65 and its a nice fast desktop kernel