Microcontroller working voltage + brownout circuit
The datasheet states that the power supply range is from 2.4V to 3.6V.
  The included brownout detection circuit triggers a warning interrupt
  below 2.2V and asserts the Reset below 1.85V.


At first glance this appears to be silly. What is the point of having a brownout voltage set below the minimum operating voltage of the chip?

However the datasheet also says "below 1.85 V... operation of the various elements of the chip would otherwise become unreliable due to low voltage.", which implies that it is reliable (though perhaps not meeting all specs) above 1.85 V.


  What happens when the supply voltage is between 1.85V and 2.4V ? Why
  the BO circuit was not designed to reset the MCU below 2.4V ?


We don't know exactly what might happen, but clearly it is expected to work well enough to respond to interrupts, and presumably take appropriate action in preparation for possible loss of supply voltage.

The BOD could have been designed to reset the MCU below 2.4V, but that would make it impossible to operate at 2.4V without risking brownout reset. That voltage would then have to be an absolute minimum rating for operation with BOD enabled, not a normal operating voltage. Which would be a problem, because the feature set includes "Single 3.3 V power supply (2.4 V to 3.6 V)". With no safety margin, how could they guarantee operation at 2.4V? 


  I'm working with LPC1769, but this applies to any MCU.


Other MCUs may be specified differently. For example the ATmega328p is specified for operation from 1.8 V to 5.5 V, and has nominal BOD voltages of 1.8 V, 2.7 V and 4.3 V. To reliably operate this chip at 1.8V you would to disable the BOD.