Their favourite person can change over time. I have always been Alfie's main/sole caregiver but I'm not always his favourite person. He took a shine to one of my previous housemates and he absolutely loves my mum, despite the fact we don't live with her. He is fine with me because I'm the only person he lives with now, so I think he just puts up with and tolerates me. I can't give him head scritches like my mum does. He absolutely melts when we go and visit her. It's sickening. 😂
We went through a period of time when Alfie wouldn't step up for me and would bite instead. There had been a lot of changes and upheaval in the house around that time and I'd also decided to cut my hair short around the same time, so I think that irked him somewhat. A couple of times he flew to the back of my head just to bite me too. It put a real dent in our trust of each other so I had to take a big step back and go back to basics with him. I started target training and if I needed him to step up I'd use a perch, as I didn't have the confidence to present my hand/arm to him in case I got a bite. I found he has a love of pine nuts so they are reserved for training only- he doesn't get them in his food. We're doing so much better now. I can't remember the last time I got bitten because we have learned to trust each other again. If I ask him to step up he will now turn or step away if he's not ready instead of biting me. He knows I will respect his space and I will give him an option to say no to my request. I still can't give him head scritches very often... but I'll take it over being bitten any day!
If your family are still keen to work with Lulu then they probably need to take a step back and stop putting themselves in a position where a bite may occur. If you know which treats she will do anything for then get your family to offer those instead of you- so that they become a bit more desirable. Lulu will probably always have a favourite person but with patience, training and tasty treats, she might come to realise that the rest of your family are ok too and stop biting. It might be best to get Lulu stepping up on a perch for family instead of hands/arms for a while. And they can use target training so they can interact with her and reward her- but from a safer distance where a bite is less likely to occur. It's really important that each of your family members are confident and calm when interacting with Lulu. If they are nervous or scared then she'll pick up on that. So like others have said, they might just need to take a bit more of a hands off approach for now and slowly start to work with Lulu to regain trust and build a relationship with her.