I figure Lucressia will also be bringing a cart or wagon of some kind along as well, to store all those trade goods that really are her purpose and employment etc etc in - so provided that's okay with mods/you guys, that might be part of the walking order. And also give people a place to ride. Maybe she and Constans could form some kind of caravan. In the event of nearly any combat, Lucressia will be diving for cover—she's self-interested, and, conveniently, using the cover of being a complete noncombatant—buuuut if some enemies end up mysteriously stabbed in the back, well, who's going to tell on her?
As far as in-camp idling, Lucressia will be busy trying to trade and profit—she'll sell crafting components and flasks and buy all that random crap you find from the corpses of the Darkspawns.
Also, IDK if this is a possible plothook/scenehook or what but it's a ~rambly idea~ that I had - she's going to be sending suspicious letters to Ignacio at fairly regular intervals. :D