It’s:
{Binding DataContext.FireCommand,
RelativeSource={RelativeSource AncestorType=ListBox}}
No need to walk up to the root unless you actually change the DataContext along the way, but as the ListBox seems to bind to a property on the main VM this should be enough.
The only thing i recommend reading is the Data Binding Overview, and the Binding class documentation (including its properties).
Also here is a short explanation on how bindings are constructed: A binding consists of a source and a Path relative to that source, by default the source is the current DataContext. Sources that can be set explicitly are: Source, ElementName & RelativeSource. Setting any of those will override the DataContext as source.
So if you use a source like RelativeSource and want to access something in the DataContext on that level the DataContext needs to appear in the Path.