Why w/o the Superkey? Is your DS flashed? If not and you aren't using some sort of passme that's likely your problem.
I haven't tried updating the EZ4's firmware in GBA mode but I would thing you can given that an EZ4 works in a GBA. The only reason an th lite wouldn't work in a GBA is the form factor. I suspect, though, that to update the EZ4 in GBA on a DS all you would have to do is select the "Start GBA game." off the DS's menu and hold down the R button... Oh, hell, let me just...
Yeah, it works. Go to the DS menu hold down R and select the GBA cart. Of course this is on my EZ4 (non-lite), but it should be the same on the lite as they use the same firmware.