Combining Webserver with LCD output

Any suggestions on allowing it to listen for web server connections and proceeding through the loop?

It's doing that now.

If you mean "allowing it to listen for web server connections" while doing other things, then move a curly brace.

// Delay   
   delay (2000);
  } // <-- Move this up to
}/* --(end main loop )-- */
   }
   // give the web browser time to receive the data
   delay(1);
   // close the connection:
   client.stop();
   Serial.println("client disonnected");

// ===========================================================
// Checking for, and dealing with, a client connection should end HERE
// ===========================================================

   Serial.print("Dew PointFast (oF): ");
   Serial.println(dewPointFast(DHT11.temperature, DHT11.humidity));