UPDATE: If you are using Maven, you can put one of the Lucene dependencies in its own project and use Maven Shade plugin to rename the Lucene references in the bytecode of the project depending on Neo4j. In my case this required moving the Neo4j dependencies into a separate project, but works great (in particular the class relocation feature).
ORIGINAL POST: It seems like Neo4j doesn't support Lucene 4 and doesn't intend to. Here's a couple informative links:
Alternative IndexProvider for Neo4J 1.9.1
https://github.com/neo4j/neo4j/issues/6
Here's the github repo where someone wrote an index provider for Neo4j to be compatible with Lucene 4. I've no idea how well it works, as I am not yet desperate enough to try it (yet), but it appears to be the only thing out there.