In this chapter she is listening to Illyrio and Varys talk about The Hands past and present. Illyrio says "If one Hand can die, why not a second? You have danced the dance before, my friend."

This seems to imply that Varys was involved in Jon Arryn's poisoning. Although, it could be in reference to any one of The Mad King's 500 Hands, I think those were killed by Aerys without help from The Spider.

Also, Varys knew that it was the Tears of Lys that killed Jon which could be evidence of his involvement. Except, we later get Lysa's confession to Petyr. Why would Littlefinger let Varys be involved in his plot / why would Varys keep the secret of Littlefinger's treachery?

Help me make sense of this.