I can tell you very definitely that L-ascorbic acid converts the Iodine in Lugol's into iodide.
You can try this yourself, with a glass of dilute L-ascorbic acid (i.e. the powder mixed with water), then add a couple of drops of Lugols.
You will notice that the brown-red colour disappears, and that when you drink it, there is no Iodine taste (there will be an ascorbic acid taste).
Now what happens when you take them separately, and at different times, is obviously more complicated.
And if you tried the above test with 100mg Lugols instead of a couple of drops, you'd have to do the maths to work out whether it would all be converted, or just experiment.