Forget About Lucid Dream?

Is it possible to have lucid dream and not remembering about it the next day?

I suppose it's possible if you have low lucidity, but not very likely. In lucid dreams, you have a higher level of awareness which makes them a lot easier to remember.

As dolphin said, it's not exactly likely. However, I'd add that it depends on your dream recall. I once woke up, wrote down my dreams, got up and took a shower. In the middle of a shower, I remembered another dream, and it was a lucid one. So it happens. :)