The query parser named lucene is Solr's most expressive and capable. With the benefit of hindsight, it should have been named "solr". It is based on Lucene's classic syntax with some additions that will be pointed out explicitly. In fact, you've already seen the first addition, which is local-params.
The lucene query parser does have a couple of query parameters that can be set. These parameters aren't normally specified though; Lucene's query syntax is easily made explicit to not need these options.
q.op: This is the default query operator, either AND or OR to signify if all of the search terms or just one of the search terms need to match. If this isn't present, then the default is specified in schema.xml ...No credit card required