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i suggest you write the microcontroller code. you first have to pass an analog signal into an a to d converter. then after conversion you can generate the required lcd codes to plot from the digital value.
I would get a screen and work out how to drive it, once you can drive the screen and draw data on it using the built in ADC is easy. My worry is that the PIC is not a very fast platform so the useability of the scope may be limited. Especially if you want to do math on the chip too, eg averages/fft like some of the new DSO's can do.