Short answers, pulled from the story.
Lucan, born Marcus Annaeus Lucanus, was a Roman poet born in Corduba, Hispania Baetica, on the 3rd of November in AD 39. He is best known for his epic Pharsalia, also called De Bello Civili, on the civil war between Julius Caesar and Pompey.
Lucan died on the 30th of April in AD 65, at the age of 25, after Nero ordered him to commit suicide by opening a vein. He had been implicated in the conspiracy of Gaius Calpurnius Piso against Nero.
Tacitus says Nero grew jealous of Lucan and banned him from publishing his poetry, while Suetonius says Nero disrupted a public reading and Lucan responded with insulting verses. Vacca and Statius suggest a deeper cause: the anti-Imperial, pro-Republic turn of Pharsalia's later books and a work called De Incendio Urbis.
Lucan was the son and grandson of Seneca the Elder and the nephew of Seneca the Younger, who raised him and likely gave him a Stoic education. He also studied rhetoric in Athens.
Lucan named his own mother, Acilia, among others before he died, apparently hoping for a pardon. His father was implicated in the proscription that followed, though his mother escaped punishment. His widow, Polla Argentaria, was later honored in a poem by Statius.
Only Pharsalia survives complete, though Laus Pisonis is often attributed to him. Lost works credited to him include Catachthonion, Iliacon, Epigrammata, Adlocutio ad Pollam, Silvae, Saturnalia, Medea, Salticae Fabulae, Orpheus, Laudes Neronis, Prosa oratio in Octavium Sagittam, Epistulae ex Campania, and De Incendio Urbis.