In this question I am not sure where the lightning is coming from. I will assume there is some source of charge at or near the archer.
From OP: "the lightning follows the arrow". But the lighting will be lost if the arrow goes too near a conductive surface.
An arrow that dragged a wire could then complete a circuit when it hit a large creature, and that would be quiet. That is basically a taser. Normal sparks ionize a path in the air. I suppose the arrow could do this. I think a path of ionized plasma would not persist for the time of an arrow flight but there is magic to stabilize it.
As I understand thunder it happens because there is resistance in the air to the movement of the current. The resistance heats the air rapidly and the expansion of the air makes the noise.
The lower the resistance the less heat. Less heat = less expansion. Less expansion = less noise.
So: if you have your arrow shed superconducting magic particles in a path behind it, your electricity would flow silently down that path to ground in your large creature.
If the arrow was too close to a conductive structure the arc would be from your magic superconducting path through the air. That would be regular air plasma with resistance and it might crackle or otherwise make noise.
If the lightning arrow really imparts a lot of energy, resistance issues in the target might make noise. Lightning can make things full of water explode because resistance in the wet thing turns water into steam, and expanding steam can blow things up. You see this most often with trees.
I have heard this once and it is loud.
If something similar happens to your large target that would not be very stealthy. The target itself probably would not notice.