To write the image, you've probably seen this one:

dd if=bsl-0.02a-floppy.img of=/dev/fd0

To replace a kernel, make certain its block count is 1360 or below.
For instance:

root@atlantis:/tftpboot/pxelinux.cfg# ls -ls
1352 -rw-r--r--  1 root root 1377420 Sep 14 19:49 vmlinuz-bsl-20050915

I haven't been able to get 1371 to fit, the magic max size seems to be 
somewhere between 1360 and 1371.

Edit lilo.conf as needed, and re-write the floppy MBR with:

lilo -r /mnt/floppy -C lilo.conf

This is assuming that you have the floppy mounted on /mnt/floppy