I agree that it's odd, but believable.
Perhaps the simplest way to accomplish /, /home, swap and working lilo would be to, now that you have lilo installed, simply reinstall the live version using the aforementioned partition structure and skip the lilo installation step. Considering that lilo is installed and working, AND you'll be putting /boot back in hda1 with the same linux kernel, it should find the installation using the existing boot record.
Delving deeper into the lilo installation problem: you mention an error message that default image doesn't exist. When lilo.conf is created it points to a specific kernel (i.e. "image"), so the error message must be indicating that the location for the kernel is not accurate. Running 'lilo -v' from the terminal (as root) should provide feedback regarding any errors that are encountered when trying to install lilo. You will find all the dirty details of how lilo will be installed by looking at /etc/lilo.conf. If need-be, you can post your lilo.conf contents along with your partition structure (fdisk -l) in a post here and we could probably help you formulate an appropriate lilo.conf that should install correctly.
Hope this helps!