A fine and moving story. It's too bad only Damon Knight, Gregory Benford, and George Zebrowski had the insight to show it to more readers.
Summary:Joe Appleby is one of several military pilots qualified to fly blood needed by colonists infected by Larkin's disease, but it will require more than 3g's of constant acceleration to get it there in time. Appleby is eligible to go back to Earth to meet up with a girl, but finds himself selected for duty, which of course he fulfills.
On the flight the primary pilot senses the flight is killing him, so he tries to talk Appleby into saying they couldn't make it. The flight confuses Appleby's senses and doesn't understand what the other pilot is saying... until the ship has been shut down. He restores the acceleration and turns off the primary pilot's controls. The pilot is killed, but they arrive in time, with Joe cognitively damaged for the rest of his life.
Relationship to other stories:
The difference, though, is that Heinlein's story focuses on the sacrifice, the greater good. Okay, you're in pain; okay, you're dead; okay, you're mentally maimed for the rest of your life; okay, you have something you'd rather do than save lives; okay, you'd rather live the sacrifice your life. But you do what you have to do to save lives. As for us, the living, our hearts break for you.
Joe Appleby is perhaps the same character--or a relative of--from "Columbus Was a Dope", who was Chief Engineer of the Starship Pegasus. He may be a relative as they are still working out faster starships in the "Columbus" story.
So far, "Sky Lift" is the only story without a clearly ironic title in the The Menace from Earth collection although one could point out that the tale isn't about skies, per se, or about anything uplifting. "The Menace from Earth" is also a tale of sacrifice, but it's voluntary. Here there the choices aren't left to the individual. Also, another sacrifice takes place in the following story, "Goldfish Bowl", another sacrifice in the name of something whose underlying purpose is not truly understood.