The concept of lineage has been a rather big headache and a cause of great confusion for a lot of people in the magickal community, especially in South Africa. There has been quite a bit of misunderstanding about what it is and how it works. This is understandable, as Traditional Wicca, as far as what is known, has only come to South Africa very recently.
Note that this statement is not referring to the many wonderful and diverse new traditions and lineages that sprang up on South African soil over the years, neither to those that may be based on Traditional Wicca, but specifically referring to legitimate Alexandrian and Gardnerian lines.
The thing is that; if you are a practicing Witch or Pagan, but not initiated into a lineaged form of Wicca/Witchcraft, there is no problem. This does not mean that these practices of a more eclectic or different path and persuasion in the great big world of modern witchcraft are any less valid. Lineage however DOES become important when some claim to be practicing initiates of traditions of, which quite frankly, they are not.
But what is lineage anyway?
At its most simplistic level, lineage is a way of confirming who initiated who, and how this initiatory line can be traced back to the founders of a tradition.
Lineage, in Alexandrian Wicca, is transmitted through the initiation rites, and would also be effected by the subsequent training. These are specific rites, containing the specific core liturgy, and specific methods of initiation into said tradition. It implies that a person was brought into the Wicca, by an already initiated member of that tradition, and that the initiator was brought into the mysteries of the tradition in the same way. As already mentioned, this also implies that this line of descent can be traced back to the founders of that tradition. In the case of Alexandrian Witchcraft, that would be Alex and Maxine Sanders.
Now in theory this should be simple, but in practice can bring quite a bit confusion.
For example, let us say A was initiated by Alex Sanders into Alexandrian Wicca. Now A works the Craft for a couple of years and initiates B. B works the craft a couple of years but then goes on to form a completely NEW tradition and changes the initiation rites, changes the names of the Gods, the components of the rite, that now barely resembles, if at all Alexandrian Craft, and initiates C into this new tradition.
Now, although B originally has Alexandrian lineage, C does not, as she was not brought into the original tradition but a completely new one. In this case, B would be the founder of a new tradition, with a completely new lineage. A good real world example would be Raymond Buckland, who brought Gardnerian Wicca to the USA, and then later found Seax Wica. A person initiated into Seax Wica CANNOT claim Gardnerian lineage, just because Raymond was one. This is the same in the case of Ordine Della Luna and Alexandrian Craft.
Another important thing about lineage that is often not realized, or perhaps not known, is that when it is transmitted properly, it would also transmit the magickal current of the tradition to the initiate, which would in turn be passed on. Without digressing into this topic, anyone who has some understanding of occult principle and the work in occult groups and traditions should realize the significance in the matter, and why it would be important in a tradition.
I hope this clarifies some of the questions about what lineage is and how it works.