In Game of Thrones S01E01, we see that Jaime and Cersei are aware that Jon Arryn was aware of their "secret". So why didn't they murder him?
In short, because they did not have to.
Jon Arryn was actively investigating Jaime and Cersei's secret when he met his untimely demise. If they were putting a plan together to murder Jon Arryn based on this knowledge it ended up not making a difference because he was killed anyway.
Look at what happened to Ned Stark: he made the same accusations and was not murdered outright. He was taken into custody and put on trial. Given that Jon Arryn was in the same position, a likely similar route events would have taken place.
The person who was in the way for Jaime and Cersei was not Jon Arryn or Ned Stark, it was Robert Baratheon... and they did have a plan to murder him...