[Spoilers Main] What would be the consequences if Robert knew that Jon Arryn was poisoned (but didn't know the culprit?)

In the books, he thought Jon Arryn died of either disease or old age but how different would it be if he knew Jon Arryn was poisoned by Tears of Lys likely informed by Ned or someone he trusted?

On one hand it would definitely make him angry and paranoid likely he would direct his wrath towards someone in the court and that point, Littlefinger and Lysa would need redirect this rage towards the Lannisters or some other party but how would they do it?