Enable the history for chat_input.

data/gui/default/window/lobby_main.cfg

@@ -411,6 +411,7 @@
 										[text_box]
 											id = "chat_input"
 											definition = "default"
+											history = "mp_chat_input_history"
 											label = ""
 										[/text_box]
 									{HORIZONTAL_SEP}

src/gui/dialogs/lobby_main.cpp

@@ -733,6 +733,7 @@ void tlobby_main::send_message_button_callback(gui2::twindow &/*window*/)
 		config msg;
 		send_message_to_active_window(input);
 	}
+	chat_input_->save_to_history();
 	chat_input_->set_value("");
 }