LCDs work using liquid crystals. The screen is divided into a grid, each pixel being a layer of liquid crystals between two conductive layers that allow a charge to be sent through the crystals. Liquid crystals work because they align themselves in different ways depending on the electrical current passed through them, since they are crystals these different alignments let you bend light in certain ways, i.e. changing the color of light that passes through them.
That means that the only thing that is actually projected through the entire screen from the edge plain white light. The rest of the "strip" is sending different currents through the screen to make the crystals in the pixels represent the right colors. The actual crystals don't emit any light, only change the light that passes through them.
Basically what I'm trying to get at is glass screen is actually the component that creates the image, so there is no such thing an LCD strip that you can attach to a plain piece of glass or whatever it was that you were thinking.