Maximising entropy generation rate via an ADC's reference voltage
To answer your original question, you can easily find the optimum value numerically using Monte-Carlo simulation. Generate a sample of your distribution clipped at 1023 for different Vref values, and use an appropriate optimization algorithm (I'd recommend Golden-section search for its robustness) to discover which value of Vref gives you the maximum entropy.

However, I believe you can get even better results if you improve your signal at its source instead of being stuck with the log normal distribution you got. I'm too lazy to do an in-depth analysis for you, but it looks that you can get a much better distribution if you run your signal through a log amp, perhaps using an offset to discard low voltage samples:







simulate this circuit &ndash; Schematic created using CircuitLab