It was announced on Thursday that Taylor will leave the club by mutual consent following Saturday's home game with Stockport after the Bantams' poor form has seen them slip to 21st in npower League Two.
Despite that, Lawn said: "Everybody would have chosen Peter Taylor out of the candidates that were available to us because of his CV.
"The simple fact is that unfortunately it just hasn't worked. We wish Peter all the best and thank him for his efforts during his time with the football club."
The Bantams board will now begin their search for the club's fifth permanent manager in the last seven years.