You're going to have to pay what you owe them. Not only does the LSDAS need the transcript to compute your grades, but the law school you end up attending will ask for a final transcript showing that you graduated before you can register for classes. There are lots of loans out there for past-due school balances. The one I used was www.teri.org
I would clear this up. You can take out a loan with TERI for a past-due balance and then defer it while you're in law school. Why would you not have paid this though? I had a past-due balance because of financial problems my senior year in undergrad, but I took out the past-due balance loan from TERI around graduation time and have paid what I could before law school starts and I defer.
Also, you have to pass a character and fitness evaluation to be admitted to the bar. They DO check education loans and such, so I'm sure they'd find out you owe your undergrad money. I doubt this would look very good when they evaluate you, and if you aren't admitted to the bar, then you've wasted 3 years in law school and all the debt you incur there.