Nolan wouldn't have touched the Lazarus pit. His entire design was to put Batman in the "real" world, as opposed to one populated by super heroes on every block. Having a pit of goo that magically brought the dead back to life, healed their wounds and youthened the old would've been about as welcome as having Superman and Green Lantern save everyone.
I do think that having Thalia be a more sympathetic character might've made more sense. Have her take over the LoS after her father's death, but hold off any immediate retaliation or continuation of her father's plans to let Batman attempt to save the city his way. At the end of TDK, when Batman is "disgraced" and accused of murder, she decides to start enacting a plan to deal with Gotham her way. A "Sorry Bats, we let you have your shot, didn't exactly work, did it?"