I have seen that cbr did a while back a lists of the
D&D Moral Alignments Of The Batman Family and
D&D Moral Alignments Of The Dark Knight's Villains
They came up with the following.
Jason Todd: Neutral
Cassandra Cain: Chaotic Good
Stephanie Brown: Lawful Good
Jim Gordon: Lawful Good
Kate Kane: Chaotic Good
Barbara Gordon: Lawful Good
Tim Drake: Lawful Good
Dick Grayson: Lawful Good
Damian Wayne: Lawful Neutral
Batman: Neutral Good
Mr. Freeze: Lawful Evil
Penguin: Neutral Evil
Catwoman: Neutral
Two-Face: Lawful Evil
Harley Quinn: Chaotic Neutral
Poison Ivy: Lawful Evil
Scarecrow: Chaotic Evil
Ra's Al Ghul: Neutral/Lawful Evil
Bane: Lawful/Chaotic Evil
Joker: Chaotic Evil
The Lists seems imo a little of when it comes to the Batfamily.
I'm fine with Dick, Tim, Damian and Jim Gordon. I would put Bruce probably also in Lawful but I think neutral also works.
But When it comes to the rest:
Jason Todd is (especially since Flashpoint) Chaotic and probably Good (but I can see an argument for Neutral).
Cassandra Cain is imo Lawful Good, can't really see why she should be Chaotic.
Stephanie Brown on the other hand is imo Chaotic and not Lawful.
Kate Kane I'm not sure but I would tend towards Lawful Good (but I think the writing might have also been inconsistent when it comes to this).
Barbara Gordon I'm also not sure id think Lawful Good fit most of her incarnations (especially as Batgirl) but a lot of the Stuff she did as Oracle was more on the chaotic side.
Selina is also imo the text book case for Chaotic Neutral and not True Neutral.