oldebloke,
Landing performance is governed by three restrictions:
[list=1][*]Approach Climb/landing climb.[*]Field Length Limit weight.[*]Certificated Landing weight.[/list=1]
By regulation an airliner must be capable of meeting the approach climb and landing climb requirements 15 minutes after takeoff, with or without a fuel jettison system.
A quick check of a field length limit chart will give you the weight limitation for Nbr2.
In an emergency, the certificated landing weight can be exceeded, up to the limits of Nbr 1&2.
Therefore, once the crew has established that they can safely land on that runway, its their decision as to the urgency. For your example of PAX heart attack or fire light, the aircraft will be capable of landing after 15 minutes, based upon a MTOW departure.
Mutt.