Is Superman gentle enough in catching Lois when she falls off a tall building?

Did you notice how  you had to "give in" when catching a ball to reduce the force from the impact? Giving in helps to give more time to stop the ball. That is really important because the change in momentum is equal to the force applied to the ball (the ball will give you that force right back so you'll feel it) times the amount of time over which the force is applied. To stop the ball, you need to remove all of its momentum. The longer you apply the force, the more momentum you will remove. If you only apply the force for a tiny amount of time, then you must compensate by giving it a high amount of force, and you'll feel it.

When Superman catches Lois falling off a tall building, he must apply an upward force on her to stop her fall. If he applies the force all at once to stop Lois instantaneously, then the force must be huge (because the amount of time is tiny and does nothing to help reducing the momentum). In that case, it doesn't make a difference whether it is Superman or the sidewalk applying that force to stop Lois' fall. Lois will get seriously hurt.

Now for the math:

(time force is applied) x (amount of force) = final momentum (zero) - initial momentum

We can estimate the time the force is applied from the film's footage. Try it below. Count how long it takes from when Superman first makes contact with Lois to when he has stopped her and is starting the ascent back up.

By my estimate, that is 2 seconds.

Lois had time to reach terminal velocity before Superman arrived. The terminal velocity for a human is around 56 m/s. The momentum is the velocity times the mass of an object (or person). Lois looks like she may be around 120 pounds. That corresponds to 54 kg. So Lois has a momentum of about 3000 kg m/s when Superman catches her.

The amount of force applied over 2 seconds by Superman to stop her is 3000/2 = 1500 Newtons. To put that in perspective, that is about 3 times Lois' weight in Newtons. To Lois, it feels like she is taking in 3 g's. Nothing that will hurt or kill her, but definitely something she will feel.