I agree with a lot of the interpretations on here, but I have another one.... This is what I thought after seeing the video for the millionth time and after a dream that I had.

Somebody has been asleep all of their life and has been searching for meaning and something to hold onto. They finally find it in somebody and long only to be with that person.... but their love is unrequited. BMTL has a desperate tone to it, which is why I think this. The lines, "now that I know what I'm without, you can't just leave me" feel like this girl has now had a breath of life and could never go back to the numb person that she used to be. She has to be with this person, but he doesn't love her back. And so she tells him that he can't leave her and asks him to bring her to life.

Finally, he sees that she needs him, but it's too late to help her. (("All of this time, I can't believe I couldn't see + Kept in the dark, but you were there in front of me")) It's too late for both of them, and they both know that. And so a part of her dies but still begs to be brought to life.

It's hard to put it into words... but yeah.