You can use a widget and this script to open the Lyrics/Chords window:
var BUTTON : Widget
On WidgetValueChanged (newValue : double) from BUTTON
if newValue == 1.0 then
ShowChordProWindow(true)
else
ShowChordProWindow(false)
end
end
Needless to say, you can then map that widget to your MIDI controller.
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Alternatively, you have this awesome extension that speaks 5 languages!
Link: Lyrics/Chords Extension
Enjoy.