I found a good way to remove the LCD without breaking it. Once you finish to clean up around the LCD just lift a bit one of the white metal backing plate and insert in the gap a plastified playing card under le LCD and slowly make your way to the center of the LCD. Repeat on the other side and the LCD will lift up intact.

to remove and put back the ribbon cable in its slot I use a piece of scotch tape. Easier to remove or insert the cable in the slot.

Since this kind of connector and very fragile and easy to damage even with a spudger I use a needle that I insert in the front side of the connector, between the connector and the socket and only apply a little pressure while lifting up the needle. The connector will then pop up from one side. Repeat the procedure for the other side. With this method it's impossible to damage the connector. I adopted this method after ruining two or three connectors using the spudger.