The panel/toolbar is called
lxpanel. It is like a adjustable box in which other little boxes or widgets can be placed...because it essentially is just that.
You can add or remove, or edit pre-defined applets by right clicking an
empty space on the toolbar. (A non-empty space will pop up a different submenu.)
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You want to add a Menu applet. There is a Menu applet already there. I'll add another
Menu to demonstrate you can create the layout you want.
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...by adding, or removing widgets.
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When a widget is added, it goes to the bottom of the list. Highlighting it, and moving it
Up or
Down, shifts the applet left or right on the horizontal toolbar.
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Having moved the
additional Menu over to the far left, you see the default icon is not the Navigatrix Ray. Edit the file to show the image you wish.
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Finally, close down the menus, having added, deleted, or edited the aspects you want.