Pope Lucius I was the bishop of Rome from 25 June 253 to his death on 5 March 254. He was banished soon after his consecration, but gained permission to return. He was mistakenly classified as a martyr in the persecution by Emperor Valerian, which did not begin until after Lucius' death.
10th century Mosaic of Pope Lucius I from the Santa Cecilia in Trastevere
Pope Cornelius was the bishop of Rome from 6th or 13th March 251 until his martyrdom in June 253. He was pope during and following a period of persecution of the church, while a schism occurred over how repentant church members who had practiced pagan sacrifices to protect themselves could be readmitted to the church. He agreed with Cyprian of Carthage that those who had lapsed could be restored to communion after varying forms of Reinitiation and Penance. This position was in contrast to the Novatianists, who held that those who failed to maintain their confession of faith under persecution would not be received again into communion with the church. This resulted in a short-lived schism in the Church of Rome that spread as each side sought to gather support. Cornelius held a synod that confirmed his election and excommunicated Novatian, but the controversy regarding lapsed members continued for years.
18th century depiction of St. Cornelius from the Church of Saint Joseph in Robertville
Cornelius by Master of Meßkirch