Again, it's irritating not to be in her lab. She's been experimenting with poisons, bacteria, and parasites for years in the privacy of the Menw, and anything here is rudimentary at best. On the other hand, just because she's developed sophisticated ways of killing people doesn't mean that there aren't perfectly straightforward ones available.
She's up most of the night. It's a relief that Anna and Aloth don't share a room; the idea of creeping around while her sister sleeps in the same room is distasteful, and this way if something goes wrong Anna won't be there to see. She does get lost trying to find his quarters, the house being somewhat enormous, but in the end she gets there before dawn.
First she sedates Aloth, with a handkerchief and some homemade chloroform. That done it's a simple matter to inject him -- she always keeps a hypo for emergencies, and the pinprick is easy to hide under the hair on the back of his neck. She lingers for a few moments to enjoy her handiwork, and then she's back to her room, hoping she can catch a few hours' sleep before anyone notices. This is something that certainly won't be on her conscience.