IN A NUTSHELL: Because it was calculated in advance. Liftoff time was known to the second and the rate of ascent was known precisely, so the camera operator compensated the delay by tilting the camera up 1.3 seconds early with a predetermined rate of motion.
THE DETAILS: In his Wagging the Moondoggie website, conspiracy theorist David McGowan considers with suspicion the spectacular TV footage of the liftoff of Apollo 15, 16 and 17 from the Moon. This footage was shot with the Rover’s TV camera, which was controlled by radio signals from Earth. Considering that the radio commands to move the camera took about 1.3 seconds to travel from the Earth to the Moon and the resulting TV picture took just as long to be received on Earth, how could the camera operator track the ascending Lunar Module? “There apparently either wasn’t any delay in the signal or NASA had the foresight to hire a remote camera operator who was able to see a few seconds into the future”, argues McGowan.
Actually, the remote camera operator (Ed Fendell) could see more than a few seconds into the future, in a way, because the liftoff time of the Lunar Module was known very precisely in advance. Exact timing was critical, otherwise the LM would not be in the right place at the right time to rendezvous with the Command Module once in orbit around the Moon. The delay caused by the Earth-Moon distance was also known very precisely. So Fendell knew exactly when to send the commands: about 1.3 seconds ahead of the scheduled liftoff time. The rate of tilt depended on the distance of the camera from the LM and had to be calculated carefully.
The first attempt at this remarkable shot (during the Apollo 15 liftoff) failed because the tilting mechanism malfunctioned and the camera didn’t tilt up. The second attempt (Apollo 16) went better, but the Rover was parked closer than expected to the LM and this threw off the calculations, so the camera lost track of the LM quite early. The third attempt worked out perfectly, and Apollo 17’s lunar liftoff was tracked until the LM became a tiny bright speck on the TV screen.