You need to do make zImage or make zlilo instead of just make. make zlilo is the best choice for most beginners as it will not only build the kernel, but also install it as the default for you if the make goes well. Be careful doing this, however, as you will lose your old kernel. make zImage will build a compressed kernel and place it in /usr/src/linux/arch/i386/boot. You must copy it to your root dir and run lilo yourself to use this one.
If you used make, you got a file called vmlinux. This is an uncompressed kernel image, and will NOT work! LILO will only boot a compressed kernel.