I think you need to lie down in a cool dark room

Are you quoting something someone wrote? As adding a comma makes things a lot more sensible:
You live once, you die once.
If you're not then I think you've drawn a false conclusion - sorry.
There is no life without death. - sort of, if a being is eternal does that mean it hasn't lived? No.
If there is no life there is no death. - yeah
You live once you die once. - No - this conclusion is false as it totally contradicts the 2nd line. Life is precursor to death, so how can you die without having lived? So the entire statement becomes a dichotomy. Put it this way how can you have drunk a glass of water without first having the glass of water.
However:
You die once you live once would be perfectly fine.
Now I'm going to have a lie down in a cool dark room