I think it all depends when did Ned meet up with his sister was that after the sack of kings landing or before. If it was after I could see him hiding the child of his sister but then Robert would not set up house with the lanniesters if Ned sister was still alive.
Ned and his crew got to the Tower of Joy after kings landing was sacked....he got there and Ned was the 1st one to see Jamie on the throne with the Mad King dead...he then left soon after because he got word that Lyanna was being held at that Tower. One assumes that Robert didn't go because he was busy with the whole becoming king thing.