Leonel Rondon Pipeline Safety Act This bill addresses natural gas pipeline safety. Among other things, the bill directs the Department of Transportation to require each distribution integrity plan developed by an operator of a gas distribution pipeline to include the risks from the presence of cast iron pipes and mains and risks that may result from the operation of a pipeline above the maximum allowable operating pressure; operators to establish protocols for communicating with fire, police, and other relevant public officials after a disaster that includes fires, explosions, or one or more fatalities; procedural manuals for operations, maintenance, and emergencies to include certain written procedures; operators to develop and implement a pipeline safety management systems framework; operators to develop and maintain traceable, reliable, complete, and up-to-date records of the gas distribution system in each region of operation; approval by a professional engineer before carrying out certain tasks on a gas pipeline system; and the development of standards that promote sufficient staffing for monitoring and regulating gas pressure levels by each operator. The bill increases civil penalties for violations of natural gas pipeline safety standards.