Assuming that LibreOffice hasn't departed too greatly from OpenOffice.org, in the extreme upper left corner of the LibreOffice header, there is an icon which displays the word Menu on mouseover (not the Menu in the toolbar). Click on that icon, and you will have a popup box with your desktops listed. Select the desktop you want the document to appear on.
In some applications, the icon is a stickpin (for setting the sticky bit). Open the document on the desktop where you want it and click on the stickpin so that it appears stuck into the page to set the sticky bit. That sticks it to the desktop it is displayed on.