The Lineage Factor is quite literally a core concept in the world of One Piece and could be explained as "the blueprint of life itself," existing in all living things. Much like DNA in our world, it was discovered by a research team led by the brilliant mind and scientist of the World Government, Dr. Vegapunk. The introduction of the Lineage Factor in the series has made most of the fantasy elements in One Piece, such as the use of Devil Fruits and genetic modifications, grounded on a scientific basis.
One of the most important aspects of the Lineage Factor has to do with its association with Devil Fruits. The act of consuming a Devil Fruit directly affects the Lineage Factor inside the eater, changing their physical structure and endowing them with special powers. Such a relationship explains why Devil Fruit powers get passed on to others after the user's death and why no person is capable of possessing the power of more than one Devil Fruit at any given time.
Throughout history, various organizations have taken advantage of the vagueness in the Lineage Factor within the One Piece world. One of the most famous would have to be the MADS study team at that time by scientists such as Vegapunk, Caesar Clown, and Judge Vinsmoke. Their research on the Lineage Factor led to great discoveries and controversial experiments.
More specifically, Judge Vinsmoke had used the Lineage Factor in his genetic modification on his children—the Vinsmoke siblings—to increase their physical strengths and give Ichiji, Niji, and Yonji special powers, effectively turning them into human versions of Artificial Devil Fruits. Sanji was a part of this experiment but did not manifest these enhancements at first glance, raising many questions as to when his probable Lineage Factor would awaken.
The term Lineage Factor has also been applied in justifying the existence or creation of man-made life forms within the One Piece world; among the most notable would be that of the Pacifistas: human weapons designed by the World Government based on the Warlord Bartholomew Kuma. It is possible to achieve such cyborgs with some tampering on the Lineage Factor of a basic human being, thus showing how the applications for such a scientific concept can actually span quite far into the series.
Recently, with the introduction of the Lineage Factor, some sort of awakening factor in one's body has been directly linked with the Devil Fruits. The case with Luffy upon awakening his Gear Fifth form, which truly unveiled the Devil Fruit he consumed as being Hito Hito no Mi, Model: Nika, has been associated with the manifestation of "unsurpassed power" within his Lineage Factor. This has largely opened up discussions about other potential hidden powers that may lie within another character's Lineage Factor.
The introduction of the Lineage Factor has also provided a scientific basis for understanding inherited traits and bloodline abilities in One Piece. There are characters with famous lineages, such as Monkey D. Luffy or Portgas D. Ace, who can be attributed with special characteristics due to their Lineage Factors. In such a way, this concept adds real depth to the importance of family lines and inherited will throughout the series.
Some critics and fans have pointed out that the Factor of Lineage is, for Oda, a shoehorning of some pseudo-scientific explanation for most of the more fantastic elements of One Piece. With this concept, he provides a framework that can coalesce into a consistent world later while retaining the sense of wonder and adventure that defines it.
The lineage factors also have many ethical questions raised against their power within the One Piece world. In a number of instances, experiments by the World Government in manipulating the lineage factor have been depicted to be morally wrong, especially in the creation of weapons like the Pacifistas. This adds some complexity to the theme of justice and abusing power presented in the series.