The Oldest Traditional Buddhist Lineage?
Every "official" Chan/Zen master (that is, a master recognized and authorized by an older master) keeps a list of his ancestral teachers going back all the way to the Buddha Shakyamuni. I have such list for my Zen Master for example. 

Every Tibetan lineage keeps a list of teachers that goes to a Buddha (not necessarily Shakyamuni). Many Tibetan texts begin by listing the lineage of the author. 

The question is moot, because every school will say its teaching is best and the most traditional.