Milly and Luke Strett decide that it's a good idea for Milly to head to Venice. Milly tells Sir Luke that Susan, Maud, and Kate are coming with her, which means Merton will also be in tow (because he always goes where Kate is, like a puppy dog).
Sir Luke asks if Kate and Merton are a thing, but Milly says they definitely aren't. This suggests she's bought into Maud and Susan's lie.
Strett takes an interest in Merton and thinks about hanging out with him sometime to see if there's anything he can "do" for the young man. Seriously, no one in this book wants to hang out just to hang out. There's always an ulterior motive.
It turns out that Strett plans on taking his own vacation to Venice shortly. So he'll be around while Milly and the gang are there.