BigQuery isn't really in the same space; it's meant for analytics queries where speed isn't as important (queries take seconds or minutes). Google Cloud Datastore is a better parallel.

Search API. Datastore isn't really aimed at search.

https://developers.google.com/appengine/docs/python/search/

The Search API is pretty much for searching text, whereas this is a database.

Also the Search API is terrible.

While I agree the Search API isn't great, it searches text, numbers, dates and geopoints. That's good enough for most uses.

I think you mean a local version, or a non-hosted version.

Right, edited the parent post.

Similarly the Azure Search appears to be a competitor to Amazon CloudSearch. I'm not aware of a Lucene based search offering from Google, however.