How many Lensman books there are is a question each fan must answer for themselves, even if you exclude later additions to the series by other authors. The original magazine serial was published as four books, but there’s a fifth book that was written as an unrelated story and later rewritten as a prequel, and a sixth book that was written to bridge the first prequel and the rest of the series. There’s also a seventh book which is supposedly set in the same universe, but seems strangely unconnected, not just to the events in the other books, but also to the setting.
Now, I’m less fond of the prequels than the original stories. They have some interesting and worthwhile material, but the seams show. I have given strong consideration to not including them, or at least including them less than the original material. In the end, however, I decided that I was going to cover the material as it exists and has been published since before the signing of the Warsaw Pact, and that means that the prequels are in, full membership.
That said, I definitely will not be including that seventh book. It really isn’t part of the same story.