How did Lady know about Vergil?

[Red]

When Lady first meet with Arkham in Temen-Ni-Gru, she saw him down on the floor, and he said to her that he was manipulated by Vergil, so Lady goes after him. Dante's 2nd fight with Vergil was interrupted by Lady, but how did Lady know that Vergil is the one that Arkham was talking about?

Probable explanation 1:
Maybe because there are only 4 people inside Temen-Ni-Gru, 2 half breeds, 1 real human and 1 who used to be human. She already encountered Dante and she recognizes her father so maybe she just used the process of elimination to spot Vergil.

Probable explanation 2:
Before she fired Kalina Ann, maybe she first watched the demon brothers battle each other. As each of them takes slashes and maybe Lady realized that the one in the blue coat is Vergil because they can take those injuries but can still continue to fight each other. Vergil is a special demon unlike those she encountered- the ones that are composed of sand, etc...