Please see the below images, it may be that some narrative events weight differently but in this case, Lillian flipped full Independence upon the conclusion of her quest.
I tried both routes, fighting her or allowing her to get the jump on the character but both provided the same Independence outcome.
This may or may not be intended or it might be a bug. As I haven't had time to do an Independence run, I can't confirm if other endings are available currently for the Inner Conflict Narrative.

