「生かんとする」 in a relative clause


These are part of the lyrics of the fifth ending theme of Hunter x Hunter (the
2011 animation).

> 朝{あさ}をむさぼり 夜{よる}を吐{は}き出{だ}し
>
> 生{い}かんとする 我{わ}が性{さが}

It seems 「生かんとする」 means 「生きようとする」:

[code]

    生く(archaic form of 生きる) → 生か (未然形) + む(ん)とする
    
[/code]

but I'm not sure whether it is a relative clause here.

Does the second line mean "my nature of trying to live", like, as part of my
true nature, I try to live? Or maybe 「生かんとする」 isn't a relative clause at all?
Since it's a song, I'm not sure.

I don't understand what "to try to exist/live" means exactly, either.
Especially since `volitional + とする` is supposed to carry the nuance of being
unsuccessful.

It seems 生く can also mean 生かす (to keep alive), so could 「我が性」 actually be the
direct object of 「生かんとする」? Can I use `volitional + とする` as a relative clause
modifying the direct object of the verb in volitional form if I'm the agent?
Like:

> 使おうとしたパソコン  
>  the computer I tried to use (and failed)

Related question about んとする: [What is the difference between ～んとする and
～とする?](https://japanese.stackexchange.com/questions/52372/what-is-the-
difference-
between-%EF%BD%9E%E3%82%93%E3%81%A8%E3%81%99%E3%82%8B-and-%EF%BD%9E%E3%81%A8%E3%81%99%E3%82%8B)

