It's a quiet calculus of problems, oppertunities, and furiously denied daydreams, as she glances from beneath the half-veil at the developments. An actual rat on the street urchin, possibly a desperate level of poor, possibly stupid enough to try for a robbery, unlikely but possible that she'd have to actually intercede. A coin given again mindlessly, worth enough to imply far more on her person or in her retinue if Azazuka's taken hostage, but the risk involved with that plan implies stupid and greedy or just swiping the purse and swimming to shore. Not worth preparing for specifically, just keep it in mind for the general paranoia of the shadowed life.

Lanterns. Fire risk, unlikely but possible on a tiny boat in a lake, able to signal with them or be a prearranged signal. Spur of the moment makes that last one unlikely, two lanterns also implies two people in case somebody else is watching and planning something. Urchin may be a surprise in their favor at that point.

Azazuka doesn't want to wait. In spite of herself, a slight surprise, only betrayed by a raised eyebrow under the charcoal gauze, barely noticable to somebody paying close attention, which her host isn't. Blackmail, trickery, seduction, all of those are possible. A brief whirl in her mind to imagining half-clothed elegance in the privacy of the lake, before her training reaches out and quashes those thoughts, focusing again on the calculus. She's not allowed to dream here.

Yes. The worst scandal Azazuka could produce from this would be nothing compared to what she'd do to herself, given the relative status between a fourth-born and the merchant-heir. Any planned seduction could be bowed out of with deferance to honor, with a swim in the lake and potentially offending her host better than serving tea at her mistress's pleasure. Onto the boat then, an umbrella over them both and a lantern in the other hand.