Ah, Rudy. In that kind of lunch scenario I would advocate leaving the actual shopping centre and going into the 'street' - there's a Wahaca, Real Greek, Jamies, etc etc. And a Shake Shack (the launch I attended with DS) which does delicious burgers and the like.
BD - other ideas, depending on what he's into -
Wellcome Collection (medical stuff),
John Soane museum (curiosities),
Geffrey Museum (homes and interiors) ,
Ragged Museum (poor people in days of yore),
Trinity Wharf (parkour training) followed by Emirates cable car to the O2 Arena,
Museum of London (generally interesting history),
Museum of London in Docklands (general history but including boats, and with added bonus of a trip 'driving' the DLR )
Etc!