(Spend the rest of my life, looking for air)
(so you can breathe, or we can die together, you and me)
Sam is so obsessed with this girl that he would be willing to look for air after strangling her (mentioned in the previous lines) and give her the air so she could breathe and then eventually die together with him.
The “or we can die together, you and me” makes the tale of Sam and Salem, a sort of Romeo and Juliet-esque tragedy of a forbidden love so strong that it transcends even death itself.
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