One - Lady shoots Dante in the head after he dangles her over a roof, so this means she's willing to shoot someone, a human, when feel threatened. Because, let's face it, she did feel threatened. I doubt Lady would ever sink to Arkham's level and kill a human, unless, yes, her life depended on it. She might be filled with hatred and revenge, but she's also morally driven.
Two - since they were half-human, this would undoubtedly present some sort of dilemma. Unfortunately, she'd probably would be compelled enough to go after them, even if they were half. But really, it's the first option - she has no absolute way of knowing they are hybrids.
Now, continuing. After Dante's speech, Lady finally sees Dante's humanity (http://www.youtube.com/watch?v=bgDiFmDLpLo&feature=PlayList&p=3ABA45DB1C4D0844&playnext=1&playnext_from=PL&index=50), she also understands the concept that, yes, even some of demonic blood can be human, and humans can be as big as monsters as humans. The whole key of Lady finally surrendering to Dante is his family issue - that is the whole turning point between the two, they have common ground. So by that, she presents him with her weapon, the name of her mother to Dante, to entrust him to go in her place to settle Arkham. She trusts Dante because of HIS family issues, his brother.
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Two - since they were half-human, this would undoubtedly present some sort of dilemma. Unfortunately, she'd probably would be compelled enough to go after them, even if they were half. But really, it's the first option - she has no absolute way of knowing they are hybrids.
Now, continuing. After Dante's speech, Lady finally sees Dante's humanity (http://www.youtube.com/watch?v=bgDiFmDLpLo&feature=PlayList&p=3ABA45DB1C4D0844&playnext=1&playnext_from=PL&index=50), she also understands the concept that, yes, even some of demonic blood can be human, and humans can be as big as monsters as humans. The whole key of Lady finally surrendering to Dante is his family issue - that is the whole turning point between the two, they have common ground. So by that, she presents him with her weapon, the name of her mother to Dante, to entrust him to go in her place to settle Arkham. She trusts Dante because of HIS family issues, his brother.