All I do is use the LM311 square wave output as pulses to a 16bit counter, and another 100mS periodic timer to count how many pulses per 100mS interval, to calculate the oscillation frequency. BTW, the PIC32 is running off a 16MHz crystal. I average the results from 5 consecutive readings, so I have a 0.5second measurement repeat rate. Good enough. It seems to be accurate enough for my needs, which is basically identifying components that I salvage, or coils that I wind myself.
LM311 oscillator based LC meter – [Link]