Is she tricking her though? That feels more ambiguous to me. In chapter 16 she told Asumi how she feels and that she wants to go out with her and Asumi said no. Then a few chapters later she says yes to being friends with benefits, but she asks Nanao if she's ok with that. Asumi knows Nanao's feelings.
Indeed, Nanao has already confessed to Asumi. The friends with benefits arrangement is just a response to Asumi telling Nanao she can't date her because she has to keep searching for Mai. That's why I don't see Nanao here as having done anything wrong, it's entirely on Asumi to sort things out. If next chapter she tells Nanao she must continue to go to brothels, I'm sure the latter will understand.