Why is lineage important? Because it guarantees us that the path that we have taken is one that has been proven to be the right path and that people have walked down that path have experienced positive results and that it is the way. If we practice something that does not have a lineage, then we would not know what the teachings are based on, and whether or not the teachings will bring any effect, or would it lead us to the wrong path. Having a lineage eliminates those risks.
It's really what my answer would be as well... although today we find many new weird, funny, new, faiths and beliefs popping out and up like mushrooms. I think BUddhism has presented it self to me the most logical, with a broken track record of results that we ourselves can see and experience from our Guru. And from there, to his Guru, his Guru, his Guru and all the way back. There is a past history, past experience, past wisdom that flows down continuously in an unbroken purity which somehow we are connected to and have the affinity with... that is why we are here in the first place... drawn to a particular lineage I suppose.
I would not look or change to any other faith... especially one without any proven lineage. It's important simply because, well I wanna know what I'm learning comes from someone who has achieved positive results for a proven record of times that it does work and I do not want to go off my nanas learning something without a proper experienced guide.
A simple analogy for me is: If we are gonna fly on a jet plane, we better make sure our pilot knows how to fly the jet and knows where he's going. And that he has done his studies with those who have experienced (his teachers are pilots too), he goes to the correct school and got his certificates and has some experience flying right? We would not hire to get on a jet with someone that has no qualifications, no clue, no background would we?