The license agreement for the DVD version of Logic is different... and only allows for you to install it on two computers (Specifically one desktop and one laptop) In additiont you are supposed to only actually run Logic on one of them at a time and not both at the same time...
So in your instance, you should, according to your license agreement, remove Logic from your older Macbook in order to install it on your new MacBook Pro....
However, if I were you, I would contact Apple to confirm this as there is some discussion as to if this license agreement is still in force or if Logic, once it is updated via the App Store Update routines in Mountain Lion, then is covered by the App Store agreement which allows unlimited installs of Logic Pro on any computer you own...
It's a very grey area... and there is nothing stopping you from installing Logic on all three Macs except for that license agreement as the physical check that used to be present in Logic Pro, to prevent you using it on more than one Mac at a time, was removed a while back... so read into that, what you will.
Again, to be absolutely sure, legally speaking, contact Apple and ask them for guidance... (and if possible get it in writing from them, if they give you the go ahead to install and use Logic Pro on a third computer)
