Okay, here's an honest question, and I'm not trying to sound pedantic or anything, but why on earth did your girlfriend continue to lean over after the dog had already growled??? I can understand why you're concerned, but try to see it from the dog's point of view. He's obviously uncomfortable with somebody leaning over him. He growls to warn that person. The warning is not heeded. Of course, he's going to bite.
First things first: Many dogs (even the most submissive ones) do not enjoy being leaned over, *especially* new dogs. New dogs HATE being leaned over. They're already trying to adjust to a new situation. Being leaned over just adds a whole 'nother element of stress. So, for now, avoid leaning over or doing other threatening movements towards him (i.e. grab of the head/neck).
As well, right now would be an excellent time to initiate NILIF, or Nothing in Life is Free: http://k9deb.com/nilif.htm
So now you know what you have to do. But if you do ever find yourself in this situation again, teach the dog "Off". If he growls, tell him to get off the furniture. Do NOT grab his neck/collar. If you must physically remove him, clip a leash onto him. In my house, new dogs do not get furniture privileges until they've learned the command "Off". This stops any unnecessary guarding.
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