The only reason I care about lineage is the fact that it was tradition in most high level styles to only pass the full knowledge to select disciples or family members. By tracing the lineage you can see who learned what, and that gives you an idea of how much you can learn. If you want to learn an entire system you would be better off finding someone who is a lineage holder rather than someone who learned some public forms. The person who teaches the public forms can most likely teach you how to fight, but your skills will be limited. Although if you train with a lineage holder you won't automatically be a high level practitioner but the potential is usually greater there