In Lego Batman 2: DC Superheroes, Batman makes the Joker robot scatter kryptonite in a large enough pattern that it could be seen from space, alerting the Justice League. So, neither Batman or Superman have any other way to contact the league, but the Martian Manhunter can call the whole league in two seconds? Wouldn't Batman have at least a dozen ways to get in touch with the Justice League satellite? Heck, later on Batman contacts J'onn and has him fire the satellite's cannon on Luthor's robot, so why didn't he call them earlier?
Maybe his League communicator was in the batcave?
Or maybe after been played for a sap so long he decided to pull a Batman Gambit just to bring Joker and Lex down a notch.
''Lego Marvel Superheroes"
For an international intelligence organization, Why can't S.H.I.E.L.D. seriously figure out that Norman Osborn is the Green Goblin?