Analog/PWM Dimming signal for a LED driver (LIPO battery low-voltage cut-off)
I think a one or two channel op-amp and a precision voltage shunt  would be your friend here.
for the shutoff, simply make a voltage divider that at 13.0V, would output an equal voltage as your voltage shunt.  Connect that voltage into the one input of the op-amp and the voltage regulated by the voltage shunt to the other.  Connect the op-amp output to the PWM dimmer.  That will take care of the low-voltage drop out.

The "work" on this circuit will be primarily in finding a particular op-amp and resistor combination to create a dimming profile that you like.  (I.E. does it dim the right amount at 13.2V, 13.3V, etc.)  To be clear, I am using the term "op-amp" loosely to include comparators and similar op-amp variants.   

Additionally, if you want to ensure that everything is 100% on at >13.5V you can use a 2nd op-amp and a second voltage divider similar to above but with reverse the hookups to the op-amp so that it switches on at higher voltages and off at lower.