In which city did Lucretius spend most of his life?

Lucretius spent most of his life in Rome, where he was deeply influenced by the philosophical teachings of Epicurus. His epic work, "De Rerum Natura" (On the Nature of Things), reflects the intellectual environment of Rome during the late Republic. The city was a cultural hub, and Lucretius wrote his poetry in Latin, making complex philosophical ideas accessible to a Roman audience. His engagement with Roman society, politics, and intellectual life is evident in his writings, which emphasize the importance of natural philosophy, materialism, and the pursuit of happiness through the understanding of nature.

The other cities mentioned—Athens, Carthage, and Alexandria—are significant centers of ancient learning and philosophy but are not associated with Lucretius's life or his works. Athens is known as the birthplace of democracy and philosophy, heavily influencing many thinkers, including Lucretius. Carthage and Alexandria were also prominent but had different focuses in their cultural and scholarly contributions. Thus, Rome is the correct answer, as it was the primary location where Lucretius lived and composed his significant philosophical poetry.