I also wear a size 4 boot and am about the same size as your girlfriend. It took me a lot of time and money to figure out that the small boot size profoundly affects a person's ability to ride well. A person with a small boot will have little leverage on the toe side of a board, so turning will be very difficult. Stick to very torsionally soft boards for her. Even mid-stiff, all-mountain boards will feel bulky and awkward.
Your girlfriend will be fine on anything between 138 and 142cm.
I personally love love love my Never Summer Pandora 140. I think it offers more than any other soft board on the market for small riders. It is flexible and easy to turn, yet the dampening (hard to find on a park board) and the RC camber allow for a very stable ride. I also love the Vario Grip edges.
So....some great boards for little people
Capita Space Metal Fantasy
Never Summer Pandora
Roxy Ollie Pop
The Ride Compact is a popular board for beginners. I'd recommend it over the Lux. A lot of people report a strange flex on the Lux
By the way, what boots is she wearing? Salomon sells a size 4 adult boot if you're looking for the right fit....