There is no such thing as a deadline to apply
for a LOC from a bank.
If you don't need it, you don't have to apply.
If you know you are going to need a LOC to finance your studies, then you should consider making an appointment with your banker or PLOC (professional Line of Credit) banker as soon as you get an offer from any law school.
You can switch law school later on. You don't have to pay anything for the LOC. Interest are charged only when you start using the money from LOC.
Once approved, you will have access to the LOC after you provide prove of enrollment
You can apply anytime. If you have enough to cover 1L, then you can apply during 1L (but not advisable just in case you don't qualify for any reasons) I suggest you apply for LOC if you think you may need it any time during law school.