If you are expecting Logol's or Iodoral to give your body the necessary Iodine part of the formula (iodine/potassium iodide), then you probably don't want to mix the Lugol's solution in orange juice or take vitamin C at the same time as any iodine.
Chem lab experiments show that:
"The vitamin C chemical gives an electron to each of the Iodine atoms to form the Iodide ion with a negative charge. This then shows that the Iodide ion is colorless in water solution even in the presence of the starch. This reaction changes the form of the Iodine element to the Iodide ions."
Did you get that? The iodine becomes a new form, iodide. You loose the benefit of iodine properties. That's ok if you only need the iodide.
The rest of the experiment will turn the iodide back to iodine; but you probably won't want or need to do this. Certainly not for consumption.
"Bleach, which contains sodium hypochlorite, removes the electrons from the iodide ion to reform the iodine element and shows the colors of the iodine element again, even if quite briefly. In the meantime, the Vitamin C is still reactive in giving electrons back to the iodine to make the colorless iodide ions.
The bleach removes the electrons from the ion form of iodine and the vitamin C gives electrons to the element form of the iodine."
The lab test certainly is not using orange juice; but why take the chance?
So, it is good, if you want to kill the taste of iodine by mixing it with vitamin C. However, remember the experiment above; and:
"The iodine is reduced to iodide, and the vitamin C (ascorbic acid) is
oxidized to dehydroascorbic acid. Iodide is an essential mineral, and
dehydroascorbic acid is just as effective as a vitamin as the ascorbic acid
Richard E. Barrans Jr., Ph.D.
Director of Academic Programs
PG Research Foundation, Darien, Illinois"