The simple Doylist explanation is that no one else can find out because it would end the plot – if brought to Robert’s or Ned’s attention, Lysa and Littlefinger are attainted for murder and conspiracy to break the King’s Peace, they’re arrested either with or without a brief siege of the Eyrie by loyal Valelords, and the Starks and Lannisters are much less likely to go to war since they’ve just almost been conned into a war – and GRRM needs the plot happen.

The more complicated Watsonian explanation is that the ease or difficulty of detecting a conspiracy depends on how many people are involved and how careful the people in question are being. Most of LF”s plot pre- and during AGOT is him working either solo or through cut-outs, or working just with him and Lysa. All he has to do is persuade Lysa to kill Jon and send the letter, and as long as she doesn’t tell anyone else (and her leaving for the Vale immediately really helps with that) it’s very hard for him to be found out unless you have LF tailed 24/7 and that’s very hard to pull off.