You can programmatically display a menu by using display-popup-menu (which is used internally to raise the context menu). The menu that display-popup-menu displays can be any properly constructed menu object, for example:
(defun popup-animal-menu (animal interface)
(let* ((items (list (string-append
"Get a picture of a " animal)
(string-append
"Send a postcard to " animal)))
(menu (make-instance 'capi:menu :items items)))
(capi:display-popup-menu menu :owner interface)))
(capi:contain (make-instance 'capi:list-panel
:items
'("zebra" "dog" "parrot")
:selection-callback
'popup-animal-menu))
Click on an item to see the menu.
You can use popup-menu-force-popdown to force a popup menu down (that is, make it disappear). This is useful for writing scripts that emulate user interactions.
CAPI User Guide and Reference Manual (Macintosh version) - 3 Aug 2017