The short answer is "it doesn't matter that much." As we have blogged about here, applications aren't read in date stamped sequential order, but rather by strength. They do, of course, have to be complete, and not having a test score will render them incomplete. Still, the lack of a score (or another attempt at a higher score) does not mean that you can't actually submit an application. Should you?
The protocol to follow here is rather simple. SUBMIT if you (1) know you are done with everything, which means no more tests (LSAT or GRE – but also please keep in mind if you have an LSAT score already, it is much more relevant to your application right now than a GRE, and there really isn't a reason to then sit for a GRE), AND (2) you have put together your very best application – not finished by an arbitrary deadline but rather when you are completely happy with how it looks. Why submit in there above even if you are waiting on a test score? While applications are most often not read by date stamp order, they are indeed date stamped. Law schools will get your LSAT/GRE score very soon after you do, so there is no reason to make them wait. Submission time does correlate slightly with perceived interest and even effort. Also, as the cycle draws longer, that completion date will start to matter more.
Barring rare nuances, it is a simple formula then. If you think you will need another test score, dependent on what your most recent results will be, or if you think your application isn't its best effort yet, do not sweat it. Use the time between waiting on your score to come out to prepare for a possible additional take or to button up your applications to the nth degree. Submit if you are done. Hold on if anything needs work.
If you have some rare nuances ask on reddit law school admissions or law school life and we'll try to find you. If you aren't sure if you are done, we are now offering a one-time application read package for an hourly rate, and we currently have availability. Always feel free to contact us at: firstname.lastname@example.org.
Best wishes toward a successful cycle!