Laurence, the son of Hugh and Estelle was a noted transportation rate authority and attorney. He attended St. Philips School and Warren Easton High School. He was employed by the Southern Pacific Railroad as an office boy at the age of 16. In 1917, he was made a member of the transportation committee of the railroad administration set up during World War I. After the war Laurence was named traffic manager of the Shreveport, Louisiana. Chamber of Commerce and in 1920 became assistant general freight agent at Houston, Texas for the Southern Pacific Railroad. In 1923 high left the railroad to establish an office in New Orleans as a traffic rate counselor. At this time he entered Loyola University where he earned a law degree and was admitted to the bar in 1928. He was actively involved in the first cases to break down southern freight rate differences and, as an attorney, frequently practiced before the Interstate Commerce Commission in Washington DC.

Laurence F. Daspit married Florence Agnes Driscoll in 1907 in New Orleans and they had twelve children, two of whom died at an early age.