Stinky output can sometimes be down to the food. What are you feeding her?
Lexi never covers her leavings in the tray. It annoys the hell out of Poppy, who will go to the tray that Lexi has stepped out of, and cover it. Poppy though, is an enthusiastic digger / cover-up-er, so yes, when Poppy has finished, it's then my turn with the dustpan and brush!
FYI, unburied leavings is the cat way of saying "this is my territory" - usually the preserve of unneutered males (feck, that reeks) and less frequently, unneutered females. Neuters will not bury their deposits if they need reassuring about their surroundings. I'm genuinely not surprised Lexi leaves her output uncovered, as she was one of 42 cats we (Ely CP) removed from one house. I guess Madam likes to proclaim that she has space to claim as her own.