She is receptive to the idea of faking an affair. Either the Nameless One can speak to Montague while pretending to be Juliette's lover, or he can give Montague a fake love letter.
There are two ways of obtaining a Love Letter:
Unless the Nameless One is pretending to be her lover, Montague will not believe an accusation against Juliette without the letters as proof.
Once convinced that Juliette is unfaithful, Montague is willing to let the relationship end. At this point, the Nameless One can reveal that it was all a ruse to add drama to their relationship (5,000 XP), or simply leave things there.
If he is told about the trick, he can be advised to play his own game with Juliette by pretending to be bored with her to keep her invested in him (5,000 XP).
After all this, return to Juliette for 10,000 XP. She will now answer any questions the Nameless One has.