Did Lysa Arryn Kill Her Husband?

While it was true that Jon unearthed the truth about the Lannisters' incestuous relationship, season 4 confirmed that Lysa was the one who killed Jon. To prove her love for Littlefinger, she killed her own husband and falsely accused House Lannister.

Why did Lysa kill her husband?

And you told me to write a letter to Cat telling her it was the Lannisters... Lysa Arryn explains her reasons for killing her husband. The assassination of Jon Arryn was a secret plot engineered by Petyr Baelish in an effort to throw the Seven Kingdoms into a state of chaos for personal benefit.

Who actually killed Jon Arryn?

Littlefinger conspired with Lysa to kill Jon Arryn (the lord of the Vale) by giving Lysa poison, which she used to murder Jon. Littlefinger had Lysa tell Ned and Catelyn Stark that the Lannisters poisoned Jon, leading to further animosity between the houses that later erupted into war.