Creating a "virtual" LED display
The nature of LCD is different from LED in that the first uses a white backlight and filters the light with liquid crystal pixels. The other is transmissive, and every pixel is its own source of light.

If you want to make an LCD look at though it is a lower-resolution LED display, you could simply design your graphics to appear as whatever type of LED display you are emulating, as you mentioned. The brightness and contrast, however are going to give away the true nature of the display to any careful observer. Even if you put the LCD behind a dark translucent acrylic and increase the brightness of the backlight to compensate, the fact that the "LEDs" are made up of small pixels will probably always be detectable. However, casual observers probably won't notice.

The effectiveness of mocking an LED display depends on your purpose: If you're doing this for a special effect prop for film or TV, it then depends on how prominent it will be. If you're doing a tight shot on the prop, shooting in HD, etc. - it might not look as convincing as it might in a wider shot. If you're trying to make something with a display that's visible in sunlight, an actual LED display will probably be much better than an LCD with a bright backlight.

What pixel pitch are you trying to emulate/achieve? What pixel width and height? For me, that would be critical to decide which display tech to use. If you're going finer than say a few mm, I recommend LCD or OLED. Above that, you can find or make an LED matrix.

The effort to back-light only specific parts of the LCD sounds as complicated, if not more, than driving a normal LED display to begin with.

(Disclaimer: I work for a company that produces LED displays down to 3mm pitch.)