Tricky.
First off, dosing Lugol's is kind of powerful and how much would you dose?
You might want to dose a little as you are deficient.
But there really are no reliable hobbyist test kits for Iodine.
What I would suggest is to download Andre Meuller's Reef Assessment Tool.
It's free and here...
https://andremueller.e-junkie.com/product/1647022You plug in any element and it will calculate your make up and maintenance dosage for each element, based on the size of your system.
Andre uses Seachem's Reef Iodide. It's cheap and will probably last forever.
Keep in mind though, Iodine is tricky. So you will want to monitor with subsequent ICP tests.
Eventually, you might consider a homemade test for Iodine. Over here...
https://www.reef2reef.com/ams/using-hanna-checker-hi-707-to-test-for-iodine.743/It's a little complicated, but I've found it to be extremely reliable. It takes the guesswork out of dosing iodine for me.