The dog gets some attention, a thorough enough rub down that would leave dog hair on the cuffs of his own coat had he not charmed all his clothing into fur-proof oblivion a long time ago. Which is the only reason there is no evidence of his own mutt stuck in the fibres of black wool. Standing and waiting patiently by the time Severus is ready, vanishing the cane sheath on his wand so that he might better plant it in coat pocket for the sake of practicality.

He frowns at the offered item, but takes it without much in the way of hesitation, as interested as he is obliging. "Will they," he says, before fastening the thing around his own wrist. "I suppose we'll soon see. Do you go by foot?"

Lucius usually Apparates, until getting uneasy at the idea of disappearing/reappearing in a chaotic field like the Fog. Then he got a broom.