I'm just guessing here, but since it was originally laced rather than stapled, the owner of the piece must be thinking that this giclee is of some value. As noted above, water based adhesives can cause problems if not used correctly.
Whatever way you plan on mounting this piece, it should be a reversible method. Granted, a mounted piece can be devalued by a potential purchaser down the road someday, but that is speculation, not a fact regarding this particular piece. Consider also, since it was laced to begin with, that it must also be a print on canvas or some other fabric material, trimming off that boarder or leaving it intact then matting over it should not affect the image itself. Consider also that it is an ink jet print to begin with, I doubt it's value will ever reach astronomical heights at a Sotheby's auction.
I would avoid any non reversible adhesives and would use a thin coat of Yes Paste and placed under glass weights over night. Excessive heat can destroy an ink jet print just as moisture can.
The way to insure your Yes Past is a thin coat is to lay your paste down with a three inch short nap painters touch up roller, then cover the wet paste with Kraft paper, then remove the Kraft, lay your print into position, cover with release paper, then glass weights. Be sure to have it on a very flat surface. Also, you must work fast, you will only have a working time that can be counted in less than a minute.
That, by the way, is the method used for mounting silk or other very thin fabrics, the Kraft paper picks up all the paste except for a very thin film that will be left on the mount board.
Good luck with your project.
-John
