That's a complicated question.
First, there's some iodine in new salt water, but if the goal is to maintain NSW levels, water changes will not suffice as it is depleted rapidly since algae and other creatures take it up.
Now the question is whether dosing it and maintaining natural levels is useful or desirable.
I dosed iodide for years, but then stopped as an experiment and nothing apparently changed. Many reefers have experienced that same effect.
My conclusions is that for most of the creatures we keep, it is an unnecessary activity. There are a few creatures, such as certain gorgonia, with a known need for iodine, but very few of the organisms we keep have a scientifically known need or use for iodine.
For that reason, I've not dosed it to my reef for at least a decade and do not think most people need to bother.
That said, it is easy enough for anyone to experiment and see if anything appears different on initiating (or stopping) dosing in their own reef.
If I were to dose, I'd dose iodide, not Lugols since Lugols contains a reactive and unnatural form of iodine (I2).
These have a lot more info:
http://www.advancedaquarist.com/issues/mar2003/chem.htm
http://www.advancedaquarist.com/issues/april2003/chem.htm