There's no pause in the conversations between the Astronauts and those on earth. If they were on the moon, wouldn't there would be a lag just like those on earth using satellite connections?
This is very true. That's why you can hear a lag. Radio waves travel at the speed of light, but the moon is far enough away for this to take a noticeable amount of time. Roughly 1.2 seconds. This means that an Astronaut would have to wait 2.4 seconds before getting a response from mission control.
So why can't we always hear this gap of 2.4 seconds?
All recordings of radio conversations of the Apollo missions were made on Earth. This means that we hear things as if we were standing beside the mission controller. The Astronaut's message comes in and the mission controller immediately responds. There is no lag because we are not aware of the 1.2 seconds it has taken the message to reach Earth, nor do we have to wait the 1.2 seconds it will take the response to reach the moon before we hear it.
Obviously the reverse is true if the mission controller is asking the Astronaut something. In this case we have to wait for the request to reach the Astronaut and then for the answer to get back. So it's the Astronaut's turn to experience no lag.
The recordings and transcripts of conversations with the Moon show a mixture of this; sometimes a full 2.4 second gap, sometimes none at all.