One of Chicago’s biggest legal aid organizations will be under new leadership this October.LAF Executive Director Diana C. White will retire at the end of June after 20 years with the organization and will be replaced by Sidley Austin LLP partner John N. Gallo.“I think he has the skills and the contacts and the desire to really take LAF to the next level,” White said of Gallo.Gallo will be only the fourth person to serve as executive director of LAF and its predecessor groups since their start in the …