Despite your profile info, you must be running 10.8/Mountain Lion, right?
All you are seeing is the standard response based on your settings in the Security Pref panel Change that to the last option and you can install/open LibreOffice (and any other app from who knows where!) without further delay.
I would advise then re-setting the prefs to Apple Store only or App Store and identified developers.
BTW, this behavior is called Gatekeeper by Apple.
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