Oh I know it wasn't his fault at all and I think if Lucy was maybe older than I would think she was utter bitch for resenting him. As it is though, I think for an 18 year old that has been constantly let down by her father, and most other people in her life in true 'Stenders style 
it would be pretty natural for her to feel a deep seated resentment for the ultimate let down.
She probably doesn't have the greatest understanding of mental health anyway, and maybe to her it was almost like a choice he made. He chose to succumb and run away just because Mandy left him. She was saddled with a hell of a lot of responsibility - don't forget she wasn't exactly a family girl in the first place. She got rid of her baby so she didn't have to raise it and now she's got bobby and a house and three businesses. And initially, no one knew he was having a breakdown, everyone thought he'd just done a runner, so already she would hate him.
I would have hated my dad at 18 if I thought he had just done a runner. Also, I think Lucy is quite vulnerable an it was easier for her to go for full on hatred than to admit that she was sad/hurting/scared.
Once she realised it was mental illness, didn't she do the right thing by removin him from a position of responsibility? Fine she could have asked him, but he was mentally ill and surely couldn't make the responsible decision? It's almost like when they had to section jean, they didn't ask her because she would have said no bit it was the right thing to do. In a way she was protecting herself and bobby because if he had left them to Ian he could have ruined them all.
I think she showed remarkable strength for an 18/19 year old - bearing in mind she was being intimidated by Derek as well.
I also think that's why she's so into Joey. He's clearly capable of looking after himself and her and cares deeply for Alice - his family. She thinks she would be safe with him.
Obviously I have a) an unhealthy obsession with eastenders and b) FAR too much time on my hands 