Hi,
You would need to find the drop-off point for charging, when the battery is charged, interpret it as a useful voltage with no side-effects/unwanted comparator trigger points and then get the comparator to turn on your LEDs. Not sure how you'd do that, though. If you are able to detect the voltage rise in the battery, then it would be as easy as setting the comparator trip point at that voltage. I add that I think Li-Ion are a bit more complicated than just measuring a voltage, it would be an idea to read somewhat more on the subject.