There are at least a couple other threads about the Li-ion batteries, try the search feature. As for all the glowing claims in the ads, what would you expect from someone trying to sell you something you don't need? If they told you the truth they probably wouldn't sell many.
The only "advantage" might pertain to those who race small motorcycles, since there is a weight advantage in that circumstance. But when you're talking about a big heavy Harley with an electric starter, any small weight advantage would be completely unnoticeable. Somehow I don't think a 10 pound lighter battery is going to make much difference in a 900 pound motorcycle. And the claims that somehow not having lead or acid makes it safer is a real joke. Look up the properties of lithium; it makes lead look pretty safe by comparison.
The charging system is a concern, and the circuitry in those batteries has been known to fail and cause fires. For instance, there have been many recalls of Li-ion batteries over the years in laptop computers and other consumer electronics products due to the fire hazard, and most recently there have been issues with the automotive Li-ion batteries in some hybrids or full electric cars. And of course they are priced much higher than the tried and true AGM batteries normally used on a Harley. Somehow I don't see any real advantages.
Btw, there are different sources for the actual cells that are inside the outer case, and some are nothing more than cheap Chinese junk. Buyer beware most definitely applies.
Jerry