Solr does not respect the HTTP headers for compression. Since it is a Web application running on top of a standard Web container, it expects the container to handle compression.
To use Tomcat's native compression, configure the following settings in the Connector section.
<Connector compression="on" compressableMimeType="text/html,text/xml,text/plain" compressionMinSize="2048"/>
See here for more details.
See here for details