To connect Tomcat to lighttpd use the following code:
server.modules += ( "mod_proxy_backend_ajp13" )
$HTTP["url"] =~ "^/tomcat/" {
proxy-core.balancer = "round-robin"
proxy-core.protocol = "ajp13"
proxy-core.backends = ( "localhost:8009" )
proxy-core.max-pool-size = 16
}