Lrr appears in a video message from Omicron Persei 8, which appears to be a "live" feed direct to Earth. In the episode When Aliens Attack, however, we learn that it takes 1000 years for a signal to go between Earth and Omicron Persei 8.
RESPONSE: Lrr is most likely not broadcasting from Omicron Persei 8, so the time delay isn't in effect. He says, "I am Lrr of the planet Omicron Persei 8," he never states where he actually is. Also, right before Lrr's broadcast you can see alien ships hovering above Earth, he is probably in one of those ships.