You say that like you don't get reasons for why the others act the way they do.With Shizune, though, you discover there are reasons behind her shotgun attitude; largely her disparate relations with her father, sibling and cousins.
In fact, Shizune's reasons for acting the way she does are almost identical to Lilly's reasons. They just take it to opposite extremes. It's actually quite interesting how similar the two of them are, although I doubt either would willingly admit it.
They both take leadership rolls because they want to help those around them, they both go out of their way to prove to others that they are completley capable of taking care of themselves, neither likes to show any weakness, they both tend to be a bit hypocritical about the things they say are most important.
Lilly just takes a more subdued path and prefers to gently guide, rather than Shizune's in your face path where she forces others to follow.