You're not chrooted into the hdd BT environment, so your re-running lilo, telling it to look at /dev/sda for the boot sector, but it's using the system map from the cd.
At least that's how it looks to me through bleary eyes at nearly 3.00a.m
So, if /mnt/sda3 doesn't exist - is your hdd BT partition being mounted by the livecd at all?? And if so, where!?
Use the "mount" command to see what you've got mounted where.
You'll soon see your BT partition, if it's there!
Make a note of where it's mounted and go back to the "chroot" part.............
EDIT:
I see you posted above at the same time as this post.
So.......
No, you're not back where you started.
You've managed to create an entirely different problem

If this is a single boot machine, I'd suggest you start again from a freshly formatted partition.......
(I'm beginning to think I should have stayed out of this one!

)