How to integrate solr or elasticsearch with JPA?
One option is using Hibernate & Hibernate search while connecting Hibernate search to Solr.
You can get a brief overview here: Combining the power of Hibernate Search and Solr
It will require some work, but not too much (1-2 days of work should be enough).
Let me know if you need more details.
Here are a couple of options you can do to keep Solr and data source in sync:
How to keep Lucene index synchronized with Mysql database?
Spring (Roo):
http://static.springsource.org/spring-roo/reference/html/base-solr.html