Lugol's is potassium iodide (KI) in water with a variable amount of molecular iodine (I2) which by itself isn't that soluble in water but which dissolves in water with the help of potassium iodide by forming triiodide (I3-). Note that this is different that, for example, tincture of iodine, which contains I2 dissolved directly in alcohol.
I say 'variable' amount of molecular iodine in Lugol's but in reality almost any Lugol's you buy commercially will be exactly the same, the 15% solution, which is 10% KI and 5% I2, providing 126 mg iodine per ml of solution. I use the Brightwell Lugol's for example, and this is what it provides (although they don't completely spell it out on the label.) It is possible to make Lugol's with more I2 although I haven't seen it but it's always worth checking the iodine concentration with any new purchase.
Fun fact: Lugol's is sold in 30 ml bottles, for hobbyist use, and not larger. Larger sizes are subject to federal regulation as precursors for methamphetamine production.