Introducing Pet Rats

Question
Hi!  I have a fancy rat that is about 10 months old named Lily the Literature Loving Rat (she lives in my reading classroom).  She is one of the sweetest animals I have ever seen.

I recently got her a companion rat, Lavender (dumbo rat).  Lavender is still a baby, although I don't know how old.  

I didn't throw them together right away, but they are now living in the same cage.  Lily seemed fine at first, but today she has attacked Lavender three times.  Lavender squeaks terribly, and cowers.  

Is this normal, or should I let Lily have her cage to herself?  They do have plenty of room (it has different levels).  Also, they are sleeping on the upper level all curled up together.

One more question:  Lavender has bitten twice and brought blood.  Once a student didn't follow instructions and stuck his finger in the cage before she got to know him (I think he startled her).  Today she bit me, but she had nibbled first, and I think she thought she was getting a treat.  But after having Lily, who has never acted ugly at all, two bleeding wounds in 2 days is a surprise to us.  Is Lavender going to be a more aggressive rat?

Answer
Its normal for them to fight a little at first, but it sounds like you do some more introductions. Put them on neutral turf like a bed. Try living arrangements again once they're comfortable with this. Also try washing or replacing some of Lily's things (hammocks, igloos, etc) so that her scent is no longer on them and she isn't so territorial. As for Lavender, you'll need to do some more socialization. Spend more one on one time with her and be patient.