Why was Elfen Lied never finished? te left us hanging for the end and it never came?

Elfen Lied was cut short (in the anime) merely because of an initial plan not to have a secondo season (as far as I know). There were a few subtle plot twists to help resolve the story about halfway through. Overall, it is a much, much sadder ending, but it is still an ending nonetheless. I'm not saying I like it, I would much like there to be a secondo season. The production value was immense... but it was just that. With the amount of viewers the mostra had, I don't think they could have afforded to go on any longer, let alone complete an entire secondo season.

I loved the anime, though, and was sad when it didn't continue. When I read the manga, I played "Lilium" whenever I stopped reading. My preferito song of all time, no doubt.

Hope that helps.

This is very common in Japan. I am pretty sure that Elfen Lied was yet another Anime that was started before the manga was finished, so they couldn't end it.