Yes, they can be upgraded through "Star-lit Crystals". Each crystal raises the internal level of the LI by one, so stats based on ratings (for a hunter, things like Blindside Crit Rating) and DPS will go up.
Don't become too attached to your LIs. You'll be swapping them every 5-10 levels. Even if you end up with legacies you really like on one, the DPS will be outdone by a higher LI with &&&&&& legacies only a few levels later. (It's usually around 6 levels.) Once you get to cap you'll want to create the perfect LI, but until then just kinda roll with whatever. Don't use crystals until the cap for sure.
Steam: Sneakeh Snake[/CENTER]