In the first book/series of ASOIAF/GOT, Ned Stark discovers that
Cersei's children are not King Robert's, but Jamie's.
He discovers it by retracing Jon Arryn's steps in discovering the secret. He finds out most of this information through Pycelle, who told Ned the final movements of Jon Arryn and even provided him with part of the proof via the book of genealogy of the Baratheons through the ages.
It is found later on in the story that
Pycelle is a Lannister spy and would want to keep the secret of the royal children's true lineage hidden.
I was under the impression that Pycelle knew what Jon Arryn had discovered before he died, particularly because Jon kept muttering "The seed is strong".
Clearly then Pycelle understood that Ned was about to discover the same truth. So why didn't he lie about what Jon was doing?
I understand that he wants to keep his true allegiance a secret, but he could have just been less helpful to Ned or feigned ignorance about what Jon was doing before he died.
Did he think Ned wasn't clever enough to figure out the truth as well? Or did he want to help him to ensure that he was kept in the loop, and would know everything that Ned had discovered?