I am no lyricist, so this is what those lines mean literally.
Singing in the night, I am engulfed by the darkness, then, the morning light shines on me.
In 朝の光がそれを照らす, "それ" means Me, singing in the night, engulfed by the darkness.
届かない could be interpreted in different ways.
I can't reach you/it
You can't reach it/me/him/her...
It can't reach me/you/us...
In many of songs written these days, the lyrics don't necessarily tell coherent story or describe specific situations but rather try to verbalise certain "moods" or emotional landscape by impressionistic (or just vague)imageries. The latter half of this passage is an example of such a case, I think.