ANSWER: The Bible record is silent regarding how and when Mary and Lazarus died. The last mention of Jesus' mother, by name, occurs after the ascension of Christ. She is recorded as meeting regularly with the disciples in Jerusalem for prayer (Acts 1:14). Mary was among the many believers who, on the day of Pentecost in 30 A.D., received God's Holy Spirit.
Roman Catholic tradition, found in their apocryphal works dating back to the second century A.D., asserts that Mary lived out her life in Jerusalem. The place venerated as her tomb is located near the city in the valley of Kidron (1913 Catholic Encyclopedia article on Mary's Tomb). Nothing is stated in such traditions regarding the cause of her death, how old she was when she died or what year she perished.
There is a major problem, however, with the Catholic supposition that Mary lived out her life in Jerusalem only to die in the city. The Bible clearly records that the apostle John was charged directly by Christ, while he was on the cross, to take care of his mother (something which would not be needed if her husband Joseph was still living, see John 19:26 - 27).
The Bible records that John was still in Jerusalem, with the rest of the apostles, in 49 A.D. when the Jerusalem conference took place. How long he and Mary stayed in Jerusalem after this date, however, is unknown. What is known is that John spent a great deal of his time at Ephesus in Asia Minor.
It is widely held (even among the Catholics) that John, after writing the book of Revelation and his release from being banished to the island of Patmos, lived out the remainder of his days in Ephesus and died in the city. Given that the bulk of his pastoral work was in Asia Minor, not Palestine, it seems plausible that he took Mary with him as he labored spreading the gospel and that she spent the last years of her life in Ephesus.
What happened to Lazarus?
Lazarus was the brother of Mary and Martha. The story of his first death, why Jesus seemed unconcerned and uncaring when told he would die, and the miracle of resurrecting him in the face of many who hated him, is a fascinating story of itself (see John 11:1 - 4, 6, 17, 20 - 21, 23 - 27, 32 - 34, 39 - 47).
There is no known Biblical record of when or where Lazarus died a second time after being resurrected from the grave. The Chief priests and other religious leaders, however, certainly wanted him to die a second time because his resurrection was causing many Jews to leave Judaism and begin to believe in Christ (see John 12:9 - 11, 17 - 19).
Catholic tradition states Lazarus was the first Bishop of Marseilles and that he died somewhere in the second half of the first century A.D. The Greek church claims his body was eventually brought to Constantinople and buried there. No other information exists.