How do I approach this? What do I tell them?
Are they going to believe me? Or think something is wrong?
If I were in your shoes, I'd use the phrase "identity theft" without going into specifics. It lends credibility due to its increased presence in our society, and at the same time, you don't have to mention LSD, LSN, or internet anything.
I agree. I'd say that it's come to your attention that someone has stolen your identity, and you would like to make sure that they don't use the information at the schools where you have been accepted to cause mischief in any way. Ask for them to put that a SSN or LSAC # is needed. I'm sure they have encountered this before. I wouldn't mention the internet if at all possible.