First of all, you sir, are insane for even touching something this microscopic.
Second off, I would use a VERY small amount of plain old super glue, crazy glue, or clear epoxy resin, around the edges of the LCD frame (apply with a toothpick etc)
Or I would use Optically Clear Adhesive (OCA) glue on the screen to bond it to the digitizer.
OCA glue is a UV activated glue that's specifically meant fo bonding LCD screens to digitizers you can get it off eBay for as little as 5$
Personally I'd go with the super glue.
Hope this was helpful! Good luck!