Whenever the priest chooses Eucharistic Prayer I (also known as the "Roman Canon"), he has the option of reciting a list of saints both before and after the prayers of consecration.
This ancient list has been nearly unchanged for centuries, except for the addition of the name of St. Joseph in the last several years by Pope Francis.
Besides the Blessed Virgin Mary and the 12 apostles, there are several men mentioned, but also several women.
These women were all martyrs in the early Church, dying by the 3rd century. Each of them was highly regarded by Christians in Rome, and many prayed for their intercession during this time.
As the Mass developed during these first few centuries, the Church chose men and women everyone recognized at the time.
St. Lucy was one of these heroic female martyrs. She had made a private vow of virginity and was turned in to the Roman authorities by a man who wanted to marry her. This led to a gruesome martyrdom, where her eyes were gouged out prior to being killed.
Her popularity spread throughout Europe, and the Church continues to honor her during the highest point of the Mass, during the Eucharistic Prayer.