I have never been able to get Linkback to work with LyX. (It's an OS X thing.) The usual method is once an object is pasted into the target application (LyX in this case), double-clicking opens the object in its originating program for editing; Saving there after editing then automatically updates the object back in the target program.
Of course, double-clicking the object in LyX opens up the LyX: Graphic dialog box instead. So one would think that control-clicking to get the contextual menu and then selecting Edit Externally... would work, but nothing happens, not even a report of an unavailable editor. What works: The Edit Special -> Paste as Linkback PDF menu is available when there is a Linkback object on the clipboard. Doing such a paste causes an image to appear in the LyX window. The image is associated with a LyX-related file with a .linkback extension. Examining the contents of this .linkback file shows that it is a PDF with some extra information after the %%EOF line that seems to relate to the originating program. There is an LyX LFUN, paste, which has a param, linkback. What doesn't work: There is no way to re-open the originating program to edit the object. There is no information in the documentation or the wiki other than "Linkback has been implemented." Jerry