How does one add an application to the LXDE Panel?

Right click on an existing application shortcut in the panel and you will get a context menu with "Application Launch Bar Settings" at the top, this is what you want. If you do not have any existing shortcuts preset... I do not know.

1) Right click on the panel and select "Add/Remove panel items".

2) Select "Application Launch Bar" in "panel applets" sub menu and click "Add".

3) This pops up a window with options to select items from. Again select "Application Launch Bar" from the options and click "Add".

4) This adds a blank "application launch bar" generally at the right end of the panel. Now click on the blank 'application launch bar". This gives you the options to assign the "blank launch bar" to your desired application from the application menu. You can add multiple applications to the same "application launch menu".

To edit this configuration manually, you need to edit ~/.config/lxpanel/LXDE/panels/panel

Thanks to Serhii Polishchuk's comment: For Lubuntu, substitute LXDE with Lubuntu: ~/.config/lxpanel/Lubuntu/panels/panel

Here's an example showing my few launch bar items:

Plugin {
  type=launchbar
  Config {
    Button {
      id=pcmanfm.desktop
    }
    Button {
      id=menu://applications/Debian/Applications/Terminal Emulators/menu-xdg-X-Debian-Applications-Terminal-Emulators-gnome_terminal.desktop
    }
    Button {
      id=menu://applications/Internet/firefox-esr.desktop
    }
  }
}

As you can see, I'm using gnome-terminal. That's exactly why I needed to edit this file manually. gnome-terminal is a menu item I can find through LXDE's menu. But unfortunately it is not visible in the Application Launch Bar Settings as described in the other solutions. So I had to put it in there manually and it works fine now.