Step 1: Understanding the event.
The question refers to the Euro crisis in 2011. The solution to avert the crisis was proposed at a summit in October 2011, and it involved the European leaders, including Jean Claude Juncker, who played a key role.
Step 2: Analyzing the options.
(A) Angela Merkel: Incorrect, while Merkel was crucial, Juncker played a central role in the actual proposals to address the crisis.
(B) David Cameron: Incorrect, Cameron was the British Prime Minister, but his involvement was minimal in the specific solution to the Euro crisis.
(C) Sarkozy: Incorrect, Sarkozy was involved but not the person whose idea led to the averted crisis.
(D) Jean Claude Juncker: Correct, Juncker, as the President of the Eurogroup, was pivotal in managing the solutions during the crisis.
(E) Lucas Papademos: Incorrect, though Papademos was a key figure, his role was later, and he was not central to the 2011 crisis resolution.
Step 3: Conclusion.
The correct answer is (D) Jean Claude Juncker, whose actions and proposals were instrumental in averting the Euro crisis.