The sudden stop is the acceleration, and it’s the fact that it doesn’t apply to everything at once that makes it dangerous. If two things have different accelerations, then they’ll end up moving relative to one another, and if the two things moving relative to one another are parts of the same thing, the thing will break.
The “aura of invulnerability” is not necessary. As usual, film, television and comic representations of Superman’s actions are produced for dramatic effect. Superman would simply catch Lois on a downward trajectory slowing gradually enough to prevent serious injury.
