When it comes to Zagreus, Lucy has an inkling of what to expect. Compassion and sensitivity is not really part of it, so at least she won't be disappointed or feel betrayed. Even if she does end up allowing him to see that she's vulnerable, there's only so much damage he can do. Well, unless he specifically sets out to hurt her that is, in which case there's probably a lot of damage he could do, but let's avoid that.

"Any idea where you'll sleep?" she asks, because that's something he should probably figure out. Bit too cold for most people to sleep outside.

And Lucy has decided to say fuck it try and figure out where it's cheap to eat, and decided to just take Zagreus to a Subway. Whatever, it's food, and they have places to sit. She steps inside it and holds the door open for him.