How to enable user search in Apache Solr?
There is the Apachesolr User module, which has just a development snapshot release for both Drupal 6, and Drupal 7. It is used from 76 sites, 72 of which run Drupal 7.

Basing on the module description, it could suit for you.


  This module will add users to apache solr. It is compatible with the latest beta of Apache Solr search integration.
  It now exposes the User entity type as an indexable entity type so it can be indexed properly. All Apache Solr hooks are available to modify the way you are indexing users.


Looking at the issue queue for the module, I found Only users with the "Bypass content access control" permission are able to search for users when Apache Solr Access is enabled. Before using the module I would rather wait that issue is fixed. If you aren't using the ApacheSolr Access module, you should not have the issue reported there. That is what a user commented.