In that case, I'm not sure what can be done then. I'm guessing they'd be able to search for an account that was created using the same IP address, but who knows.

Knowing that you're dreaming is the very definition of being lucid - you don't have to have control of the dream; you just have to be aware that you are asleep! So in that case, I'd definitely say it was an LD, if not one with lesser control. Most people exhibit control in some of their non-lucid dreams (flying, slaying dragons, walking on air), but they aren't lucid. Others can be lucid and have no control. Sometimes dreams just don't seem that controllable, but luckily these aren't very common; acively practicing control is another thing you can do.

If you want to DILD, feel free to have a read through my guide. Awareness and mindfulness are a very important part of lucid dreaming (being 'lucid' is just another word for being 'aware'), and the guide has a few pointers on how to go about maximizing your DILD chances.