When you exit LO "normally", all temporaries are deleted. After all, you may want to discard your session work. There is no reason LO would override your decision (even if it is a blunder) on its own.
In case exit from LO was "abnormal" (a crash, power failure, etc.), temporaries and recovery information are still there. Restarting LO initiates recovery and you may recover your document in some previous state but latest state is not guaranteed (some edits may be lost).
Conclusion: if you don't save your document, you can't recover it. This statement is valid for any application.
However, depending on your OS (which you didn't mention) and the filesystem category, you could use highly specialised utilities to salvage deleted files (targeting the LO temporaries) but chances of success are rather low. I add that the amount of work involved probably is not worth the pain compared to the time needed to retype the document.
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