I am unaware of any biblical support for the claim that Mary Magdalene was related to Lazarus
1) She was a supporter of Jesus and had been healed of demon possession. Luke 8:2-3
2) She was one of the women who watched the crucifixion from a distance. Matthew 27:55-56.
3) After the crucifixion, she stood beside the cross with His mother, John 19:25
4) She was with the women who visited Christ's tomb Sunday morning. Matthew 28:1
5) She was among the women who reported the resurrection to the Apostles. Luke 24:9-10
6) She saw the risen Lord and announced that fact to the disciples. John 20:18
OTOH, one of the claims made about Mary Magdalene does not fit with other early sightings, found in Mark 16:9. Since this section of the book is under a cloud, conservatives do not support this claim, because it is not supported anywhere else.