Stuck at Lady Boyle's last party

To non-lethally remove Lady Boyle, you need to help Lord Brisby abduct her. Speak to Brisby (he's the one in the hideous mask) and he'll tell you he's in love with her and to bring her to him in the cellar (which will add his location as an objective).

Identify the correct sister and bring her unconscious body to him. Luring her to the basement is optional but makes this much easier.

Dishonored is quite robust when it comes to doing things in the wrong order- speaking to Brisby then giving him the already unconscious Boyle should work. If not, you will need to load an earlier save.