Ehm I'm not sure. I got a random e-mail from them on March 5th saying my application was "Still UnderReview." I was admitted March 28th. Idk if this helps you but that was my timeline.
"Complete" means that they have received all of the necessary forms for your application and "underreview" generally means that they have opened your file but have not made a decision yet.
If you go to the test that you're scheduled for and click on it it will say "file underreview" or something else. I emailed accom@lsac.org. It's listed on the website and they got back to me within 2 business days