Many Lovebirds, as well as other parrots, will defend their cages (homes) when an intruder enters it. It's normally just confined to inside the cage. I don't think I've ever had a bird that will defend the outside of the cage. Respect his attitude and work around it. Once he comes out, everything is fine so don't sweat the small stuff, so to speak!
I'm glad to hear that he is spending time with your girlfriend. I have some that will spend some time with other people but I'm still the main slave.....
I am so glad that this is working out and you didn't resort to desensitization. As you are finding out, you can't force trust. It has to be earned!