At some point in his life Lucretius became attracted to Epicurean philosophy. Like other Epicureans, Lucretius believed that even if gods created the world, the normal workings of the world - day and night, weather, eclipses, births - happened naturally, and gods had nothing to do with it. Death, in Lucretius' view, was just the end of awareness. He didn't think there was any afterlife at all; you should compare how you would feel after you died with how you felt before you were born.
The afterlife was an important question for Lucretius because during his lifetime a lot of people in West Asia and the Mediterranean were first beginning to believe in an afterlife with Heaven and Hell. Not just Epicureans, but also Buddhists, Zoroastrians, Christians, Platonic philosophers, and Gnostics were all very much concerned with the afterlife around this time.
Lucretius also believed, like other Epicureans, that everything was made of tiny particles they called atoms, that combined in different ways to make different things. This turned out to be right, but Lucretius didn't have an electron microscope, so he didn't know it for sure - he only knew about atoms as a theory.
Lucretius' main achievement was that he wrote a long poem, On the Nature of Things, about Epicurean philosophy in Latin, where before it had existed only in Greek. This made sure that Western philosophers who didn't know Greek still understood the principles of Epicurean thought.
Lucretius probably died about 54 BC, when Julius Caesar was beginning his career. Lucretius died young, when he was only about 43 years old. He probably died without finishing his great work, because even though it was published parts of it seem to be unfinished. Cicero and Virgil, among others, read and appreciated Lucretius' long poem after he died. But soon afterward, as more and more people began to have faith in an afterlife, people forgot about Lucretius, and he was mostly forgotten until people rediscovered his poem in the Renaissance, 1500 years later.
To find out more about Lucretius, check out these books from Amazon or from your local library: