I still believe that the low heart rate is a symptom of hypothyroidism as palpitations , and shortness of breath +++.
There is quite a lot of potassium in Lugols; this can slow the heart for a while; this is where the salt comes in.
Try to take some good salt together with your Iodine and see what happens. Iodine works over a bit of time; and sometimes you can have a worsening of the symptoms for a while before the situation is better all over.

http://www.umm.edu/patiented/articles/how_serious_hypothyroidism_000038_6.htm

"Hypothyroidism may slow the heart rate to less than 60 beats per minute, reduce the heart's pumping capacity, and increase the stiffness of blood vessel walls."

http://en.wikipedia.org/wiki/Hypothyroidism

"Less common symptoms

* Impaired memory[12]
* Impaired cognitive function (brain fog) and inattentiveness
* A slow heart rate with ECG changes including low voltage signals. Diminished cardiac output and decreased contractility."

http://www.cure-hypothyroidism.com/symptoms-of-hypothyroid/

"Short of breath - Respiration will also be slowed.
Vital signs are likely to be subnormal in individuals with hypothyroid. Symptoms of hypothyroid, such as slowed heart rate (bradycardia) and decreased contraction of the heart results in diminished cardiac output."