Lavaliering doesn't mean that you're "virtually a brother," at least that i've ever heard of. Do a search on lavaliering, you'll find it's been discussed MANY times.
Basically it's like a pre-engagement. Usually goes lavaliering, pinning, engagement. Although pinning isn't used as much. It symbolizes more the relationship between you and your BF than you and the fraternity.
They're not going to tell you any secrets or anything. Of course if you want to find out a lot about the history, etc. most of that is not ritual and all you have to do is ask them and i'm sure they'll provide you with the info. They'd probably find it quite flattering that you wanted to learn more about their history.
But you're not "entitled" or "priviledged" to anything.... besides your boyfriend's love and affection, of course. And hopefully some amount of respect from the rest of the house, but of course that can't be guaranteed.
Some guys get a little POed when one of their brothers lavaliers a girl. Actually in some houses the guy doing the lavaliering gets a lot of crap about it. At least that i've seen firsthand.
Good luck to you and your boy.