PoorQuentyn fielded this question on his blog a couple days ago:
Do you think Varys set up Tyrion to kill his father? If so was Varys planning on releasing Tyrion on his own even if Jaime hadn’t made him do it?
To which PQ answers:
Yes and yes.
I was unfamiliar with the idea of Varys having set Tyrion up to kill Tywin, but a little Google search reveals there’s plenty of support for it.
It did occur to me some time ago, however, that Jaime was not the one who came up with the plan to free Tyrion. No, that plan depended on Varys, and if Jaime had, for example, gone back to Casterly Rock on Tywin’s orders, Varys still would’ve gotten Tyrion out of Dodge. Jaime may have even thought it was his idea to free Tyrion, but ultimately it would’ve happened with or without him.
Now, what Varys didn’t know would happen with Tyrion’s liberation was that Jaime would tell the Truth About Tysha. And Jaime never imagined that Tyrion would respond by following their father into the privy with a crossbow, but according to the theory of Varys setting up Tywin’s death, Jaime’s telling that story just happened to be playing right into Varys’s hands.
However, because Jaime was still serving in the Kingsguard and still present in King’s Landing, he helped Varys with freeing Tyrion. Because Jaime was involved in Tyrion’s liberation, he decided to divulge the truth about Tyrion’s first wife, and confess his complicity in the way she was punished for being lowborn. Because Jaime told the Truth About Tysha, Tyrion is now talking like he wants to kill Jaime along with Cersei. Because Jaime was there to help with Tyrion’s liberation, and because of the way Tyrion reacted to the Truth About Tysha, Jaime blames himself for Tywin’s death.
Finally, because Jaime didn’t quit the Kingsguard when Tywin asked him to, Cersei effectively becomes Jaime’s boss following the death of their father.