'Drying' in a normal vacuum dessicator will have no effect, as LiI is very hygroscopic. The only literature references I could find on making the anhydrous salt from the hydrate involved prolonged heating (2 days or so), high temperatures (around 200oC if I recall correctly), and high vacuum. This may have been slight overkill, but all the references I found were along those lines. I would suggest you chuck it after one use, assuming you're only using it in catalytic amounts (I know it isn't cheap).
The cheaper and less hygroscopic lithium perchlorate may be an alternative option, depending on what you're using it for. It can be dried under vacuum in 2 hours at 140oC, just be sure to thoroughly free it of all oxidisable impurities before heating it. See the thread Post 422345 (https://www.thevespiary.org/talk/index.php?topic=11800.msg42234500#msg42234500)
(Kinetic: "Friedel-Crafts acylation with LiClO4 catalyst", Novel Discourse) and the link in my post below it, which should tell you whether you it's suitable for your purpose.