Lucene:
Apache Lucene is a high-performance, full-featured text search engine library written entirely in Java. It is a technology suitable for nearly any application that requires full-text search
Solr:
Solr is an open source enterprise search server based on the Lucene Java search library, with XML/HTTP and JSON APIs, hit highlighting, faceted search, caching, replication, a web administration interface and …
Essentially, Lucene is embedded in Solr and is purely a full-text search library, with the purpose of being embedded into projects giving them full-text search capabilities. Solr has much more features and administration capabilities, allowing to search structured data without needing to write any custom code, load data from CSV files, tolerant parsing of user input, faceted searching, highlighting matched text in results, and retrieving search results in a variety of formats (XML, JSON, …) .
Check Solr features page and see if any feature is relevant for your project.