The name, Lazarus, means "God has helped".
Jesus knew his father Simon, whom some identify as Simon the Leper, and used to visit their home every time he was in the area, developing a close friendship with Lazarus, who followed his teaching and ideals. He became a friend of Jesus who raised him from the dead (John, Chapters 11 & 12).
The church survives today.
The second mention of a person named Lazarus was in a parable in which Jesus describes a common scene of a poor man begging. (Luke, Chapter 16, vv. 19-31) He is described as being "full of sores" and is generally thought to have been suffering from leprosy, the disease being endemic in the Holy Land at the time. Here Jesus uses the name ‘Lazarus’ in the generic sense of someone whom God helps while others ignore.
Both episodes were probably taken into account when the monks of St Basil originally selected a name for their leper hospital. The name eventually gave rise to the terms "lazar", meaning a leper, and "lazaretto", a leprosarium, or Leper House. The gate of the city of Jerusalem by which the St Lazarus hospital was established is still known today as the St Lazarus Gate.