Solr can be run on Windows Azure, using a simple installer that is available for free download. See the documentation for the Solr Installer for Windows Azure for information about how to deploy Solr/Lucene on Windows Azure web roles and worker roles, using multi-instance replication for index-serving and single-instance for index generation with a persistent index mounted in Azure storage.
Typical scenarios addressed with this sample are commercial and publisher sites that need to scale traffic with increasing query volume and need to index a maximum of 16 TB of data requiring a small number of index updates per day.