Thanks for taking an interest.
I would say that we're most comparable to Lucene, given that we're a library not a server. But, we're also very much not a port of Lucene to go. That already exists, and someone has posted that link elsewhere in this thread. I've worked a fair amount with Elasticsearch, so a lot of the higher level API is inspired by it. And thats one of the biggest differences between Bleve and Lucene today. Lucene is pretty low-level. The bleve top-level API works a lot more like Elasticsearch (specifically there is a mapping, its serialized and stored in the index). There is a lower level that looks more like Lucene (everything is just documents and fields), and the top-level API builds on top of that.
That is I would say the primary goal of Bleve, to be a great text indexing and search library for Go.
Next you asked about a REST interface. Bleve ships with HTTP handlers in a sub-package. These are completely optional, you can use Bleve without them, or you could write your own if you don't like these. There is a not-quite-done-yet example app that uses these to make it look a lot like a single-node Elasticsearch. But, its just an example app, I have no immediate plans to try to turn this into a production app.
Regarding scaling beyond a single embedded instance... Obviously there is a lot of interest in this area. The way I'm looking at this right now is that this is simply a layer above Bleve, much as Elasticsearch/Solr provide this as a layer above Lucene. There are a few enhancements we could add to streamline this, like allowing the Searches to operate across multiple indexes.
My hope is that lots of apps spring up around Bleve. Maybe someone wires up the HTTP handlers and Raft and makes an Elasticsearch clone. Maybe people will do something I don't expect. Will we go there? Not right now, we've got our hands full. But if we do, it will be in a separate project, built on top of Bleve.