What does it mean to calm my life and make me feel lonely and fleeting?

This sentence means spending your lonely life with elegant and quiet music.

"A quiet voice that soothes me all my life" means that I hope someone can spend my life with elegant and quiet music. Here, "soothing voice" can be understood as both music and clear and pure state of mind. "Drunk My Lonely Time" expresses the author's feelings about lonely time and is willing to spend his life with his partner in this romantic atmosphere.