Citadels - Can a warlord destroy a district for free?
Yes.

This is explicitly stated in the rules.


  8) Warlord
  
  You receive one gold for each military (red) 
  district in your city. At the end of your turn, you 
  may destroy one district of your choice by paying 
  a number of gold equal to one less than the cost 
  of the district. Thus, you may destroy a cost one 
  district for free, a cost two district for one gold, 
  or a cost six district for five gold, etc. You may 
  destroy one of your own districts. You may not, 
  however, destroy a district in a city that is already 
  completed by having eight districts (or seven 
  districts when the Bell Tower is in play).


[Emphasis added]