When it comes to being raised by Gaffer Hexam, Lizzie is like a flower that has grown out of a compost heap. Despite all the terrible treatment she gets from her dad, Lizzie is so kind that she remains devoted to the man. She no doubt figures that if she weren't around to take care of him, he'd be an even worse person. As she tells her brother Charley,
So there am I, Charley, left alone with father, keeping him as straight as I can, watching for more influence than I have, and hoping that through some fortunate chance, or when he is ill, or when—I don't know what—I may turn him to wish to do better things. (1.3.165)
Right up to the moment Gaffer dies, Lizzie is convinced she can make him a better man. Even when she hears that her father is a murder, Lizzie always assumes the accusations are false (which they are). As the narrator tells us,
Of her father's bring groundlessly suspected, she felt sure. Sure. Sure. And yet, repeat the words inwardly as often as she would, the attempt to reason out and prove that she was sure always came after it and failed. (2.6.88)
This hardcore loyalty is something Lizzie eventually brings to her marriage with Eugene Wrayburn. Even though Eugene is disabled after his near-murder by Bradley Headstone, Lizzie nurses him back to health and spends every waking moment caring for him. There's no doubt that in Dickens' eyes, Lizzie is an ideal woman. Modern readers might question, though, whether all women should spend their youth supporting men like Gaffer Hexam.