Whether your teacher needs a long lineage behind his art is a decision entirely up to you. But one thing is certain: if your teacher claims a long lineage, he should be able to back that up in some way. I've seen many, many teachers on this forum and in real life who claimed elaborate lineages going back centuries and who turned out to be total frauds. Some of them were martial arts jokes, incapable of fighting their way out of the proverbial wet paper bag. Some of them were actually decent fighters with something to teach. But all of them lied.
No matter how good an instructor is, if he feels that he has to lie about his own training then that raises certain questions. On a basic level, how can you trust a man to safely teach you potentially dangerous techniques if he can't tell the truth about his own training? On a broader level, our teachers make a huge impact on our lives, even when we don't realize it. In Old School, Ellis Amdur recounts a conversation with Hung I Hsiang. "Be careful with whom you choose to study," Hsiang told him. "You will become who they are, and if you haven't chosen wisely, you'll suffer and other people will, too." Anyone that you spend as much time learning from as you will with a martial arts instructor is going to have a significant influence on your life-- I've seen this in my own life and in the lives of others. If your chosen teacher is a person who builds his life on deceit and if your whole interaction with him is based around a fraud, that can't have a positive impact on your life.
David Sims
"Cuius testiculos habes, habeas cardia et cerebellum." - Terry Pratchet
My opinion is, in all likelihood, worth exactly what you are paying for it.