Where does Quicktime store its screen recordings?
As of OSX Sierra, it's here:
~/Library/Containers/com.apple.QuickTimePlayerX/Data/Library/Autosave Information
In there, there is a container/package/directory called Unsaved QuickTime Player Document.qtpxcomposition that contains a Screen Recording.mov file with the actual video. You can copy-paste that mov file wherever to save it permanently.
You can also double-click the Unsaved QuickTime Player Document file directly. That file opens in QuickTime, and allows you to save in a proper place. Note that sometimes QuickTime will fail to save a Screen Recording with the error "The operation could not be completed" (using File > Export As might work, though), so copy-pasting is probably less prone to error.
My battery ran out when I was recording and found my file there.
As of Catalina, I found my recording under ~/Library/ScreenRecordings
Although the recording did stop when closing the lid, it does not mean that the recording is saved.
If it is, by Command clicking on the file's name, the full path where you can find it will be displayed.
The default storing place, of course, is under ~/Documents.
The screen recording movies are saved in the "Autosave Information" file if you didn't save them or close them manually. I stumbled on it a while ago, and believe me its not easy to find. They are located in a hidden "Library" file. The only way I found it was by searching for "autosave" in Finder, and I was able to recover my lost screen recording! There are several of those "Autosave Information" files for different apps like Chess, and Quicktime! But the specific "Library" file (where the autosave file is located) is hidden (at least on my computer) so, like I said, you can only get to it by searching for "Autosave Information" in finder. If you have any files autosaved, they would be there. I was able to recover my files there. Also I should mention I found my screen recordings there after I had to restart my computer without originally saving them. Such a relief!