The Law Education Programs are great....one of the pilots in my squadron got picked up for LEP, went to University of Chicago law school (with full Navy LT pay and allowances) and then got picked up for an MBA program along the way. That's one of the things that got me thinking about going to Law School... I applied for LEP and was the second alternate the last year I was eligible, so I got out and went to law school on my own.
Hoops has a good point. Sure, going to law school on an intermittent, night school basis between your operational commitments is probably possible...but your military job comes first, and you get out of law school what you put into it. Law professors aren't going to cut you any slack because you had the mid-watch the night before (and in fact, used to prey on those that were unprepared ...I suspect even law school has gone the way of kindler and gentler). Credentials (school selection and class rank) are really important if you want to work at the BIGLAW firms , or even inhouse with some major corporations, so you will be giving up opportunities if you try to get through law school while on active duty.
Finally, this is the second thread in just a few days focusing on grads trying to set themselves up for their next career. I truly hope that this is not indicative of candidates , current cadets and midshipman, or recent grads viewing a Service Academy as a stepping stone rather than an opportunity to serve. Of course, I recognize that not everyone is going to serve a 20+ career (I didn't), but during the early stages in your career, you should have an open mind about the future and focus on being the very best officer you can be ... There is plenty of time to worry about follow on degrees and careers. I know it may not seem like when you are 22 and just starting out, but those 5-7 years as a Junior Officer may well be the most fun and rewarding times of your professional career. I look back (almost 30 years now), and wish I could be back flying as a P3 crew in Iceland again !