ground to ground that would be the ground of LM4863 (pin2,7 and 15) to Arduino's ground, right?
Right.
I am just wondering why do you say to connect the arduino analog input to Lout- or Rout- of LM4863 and why not to Lout+ or Lout+
I was thinking distortion level 'd be less on those pins (5, 12), compare to 3, 14 where second inverting amplifier implemented. Shouldn't be much difference, 1% isn't an issue for your application?
If you want to play safe , put a resistor in series with arduino analog input, 5-10 kOHM, that 'd save arduino if you made mistake with polarity