Browser support for dragging events is rather limited and one-way.  You can drag documents from your machine into a browser (if the particular site or application allows it), but that's it.  You can't drag out of the browser and you can't drag between browsers.  You'll have to export the document from the Laserfiche web client (Web Access), which will allow you to save it to your computer.  Then you can upload it to the other web site (either dragging or with a file selection dialog).