What were the circumstances of the lisbon earthquake of 1749, and what trauma did it pose for both orthodox christian theology and philosophical optimism? (what features are in common between the two outlooks, that you infer that voltaire is hostile

I believe you are referring to the 1755 Lisbon earthquake.

On November 1, 1755, the greater area of Lisbon was destroyed by an earthquake, which was followed by a tidal wave which destroyed the shipping in the river Tagus. Around sixty thousand people have lost their lives.

This occurrence sparked a lot of discussions involving both religious and philosophical questions. Two main point of views are Voltaire's and Rousseau's.

Voltaire examined evil and suffering related to the disaster. He had made the connection before, pondering onto previous earthquakes, such as prior earthquakes in China, Lima and Callao. He thought that God's rules were not meant for man's best good, asking if it has been the will of God or if could it have been vengeance. He also reflected on why Lisbon, if Lisbon was worse than other cities and if there were worse sins or more evil in Lisbon than other cities. Finally asking if god is the culprit of these catastrophes, even though he is supposed to be love and kindness.

Rousseau on the other hand had more systematic views of the world and man. Rousseau believed man is good by nature but is corrupted in contact with other men, the only solution being to return to nature. Rousseau represented the optimism views and and considered Voltaire's poem on the Lisbon earthquake both a personal attack on him and a lack of understanding and distortion of God's preponderant action.

The common ground is that neither one of them were atheists, both believed that God existed, but diverged on the nature of naturally good (Rousseau) and evil (Voltaire).