Definition of fall on:
(v) :
(of a holiday or event) To occur on a particular day.
(v) :
To be assigned to; to acquire a new responsibility, duty or burden.
(v) :
To experience; to suffer; to fall upon.
(v) :
Of the eyes or gaze: to alight upon.
(v) :
(archaic) To attack (someone); to join an attack on (someone), especially a surprise attack.