Lineage to me matters only in certain cases. That is when your claim as membership to a certain group, that is oath-bound and initiatory based, needs to be verified. Of course lineage is only one way to do this. But that is as far as I think it should go. It doesn't make you better or more legit, it just shows you are a member of said group or at least you were at some point. The threads of tradition flow through many avenues, many of which are not 'lineaged' sources.
Don't get me wrong though. I place a great deal of weigh on training and tradition. Its just far too often that lineage is thrown around outside of the circles it matter in. Just as membership is not external to the group neither should be one's lineage.
"Lost in a thicket bare-footed upon a thorned path."