How can I create a new menu entry for the panel for Lubuntu (LXDE)?

On Lubuntu's panel, I can add the "Directory Menu". When clicked, instead of opening an app, it shows a menu (which in turn can open an app). See the image:

EDIT for clarification

In the image, the desktop is blue. I have not clicked the menu icon (the blue bird on the far left), but instead the Directory Menu icon, where my cursor is showing. The menu below it (bin, binConf, …) belongs to that icon.

(The Directory Menu is added to the panel by going to Add/Remove Panel Items, and adding Directory Menu.)

I want to create my own menu icon (not for files, though). Having searched all over the place, I can find how to create new panel launchers, but not new panel menus.

How do I go about making such an entry for the Lubuntu panel?