Because it interoperates with Maven. It can fetch and install code from Maven repositories, can read and write a pom.xml file, and uses the same groupId/artifactId/version format for specifying dependencies. And it also depends on a few org.apache.maven packages. So without looking at the source it would be easy to mistake lein for a Clojure wrapper around mvn. But it's more like a Clojure implementation of a superset of Maven's functionality, I guess.
You and I are definitely both correct about it being a dependency: it caused me some installation headaches. I may have misunderstood the docs about how deep of a dependency it is; I haven't read the source.
Returning to the OP's point, given that it is a dependency, it's still possible there is some resulting startup overhead, but I couldn't say for sure without profiling it.
My biggest headache with it was just figuring out how to tell it to use a local jar. It really wanted to fetch it from clojars or maven central but sometimes you just need to use a jar that's sitting on your hard disk. IIRC there's no standard way to do this and I had to create a local maven repo for lein to pull it from.