Oh God...... don't take the lyrics down. Look at the discussion about this important subject you have sparked.
AND... as you say, the song isn't intended to be about a final result of suicide. It's intended to be about the feelings of hopeessness that leads to it.
THAT is an utterly and vitally important subject. And it's incredibly difficult to capture the one without evoking the other.
My suggestion would be to keep working the song (usually best done after setting it aside for awhile) and then work to provide readers/listeners some insight that lets us in on that intent.
And.... fwiw... even though it doesn't imply suicide.... "Can't live if living is without you" is (like many love songs) frightfully dysfunctional in it's own right.
Fixating on another person as "necessary to an extreme" is a staple of love songs, but in real life, it very often leads to tragedies. In many songs AND movies, there is a fine, thin line between stalking and true love. As a counselor, I'm sure you have seen that.
While I personally am biased against anything that can be perceived as "promoting suicide", I would NEVER wish to be an agent of censorship and prevent other people from communicating thoughts outside my own bias. I would feel terrible if you were (even voluntarily) prevented from communicating your experiences because of my personal bias.
Again.... I REALLY hope you do not take this lyric down. It's a great lyric with just the one (unintended) mis-communication. Fix it, don't remove it.
Really, since our/your intent with every lyric is to "have an impact" this is probably one of the most effective lyrics ever posted here. This is what writing is all about. You have "provoked thought."