Awesome, thanks for your help Agriba!! Good points. I have changed it based on your comments, hopefully it works better.
An immortal assassin, sick with self-loathing, craves death. A child’s love heals his hatred, saving his life. He must now return the favour and save her from the gallows. Death, once lusted after, must now be denied.
Interesting, but you haven't resolved how/why an immortal is now in danger. Is the immortality tied to assassination? I.e. Taking a life transfers the 'lost years' to the assassin?
Also, "A child's love" could be misinterpreted.
(I'll go out on a limb here... if none of this actually works for your hook, take it as feedback that I missed what your story is about)
After assassinating a girl's family, the child's compassion shocks Jack-the-ripper [or name of assassin] from the self-loathing that's been building for the last two thousand years. The trouble is that she's going to hang for his crime unless he saves her.
When a girl convicted of murder saves Jack-the-Ripper from his self-loathing, he has to choose between suicide and rescuing her from execution.
Remember, you want to convey who the character is, what's at stake, and the essence of the plot. Being immortal is cool, but you need to determine if it's important enough to include in your hook.
I used "Jack-the-ripper" to illustrate that the right name can convey A LOT of information.
Hope that helps!