Getting info on the first try wouldn't inform us much, though. Assuming that she is telling the truth about her passive, the large margin of votes on her wouldn't help us narrow down on any suspects that easily. Lynching again on the second try in the council, may or may not fail because the assumption in this case is that she's telling the truth. In which case, the second info isn't guaranteed.
On the assumption that she's scum and lying about this while in actuality having only a single lynch save or none at all, then prioritizing both, Xlaw, and Nana is better here. If Nana survives the council, making her flip and from her role may give us info on the council, and if she fails, well that's a win. We put ourselves in a position where we have/can effectively eliminate two scum reads that wouldn't keep pinging us at the back of our minds if left otherwise.