Born in Minnesota, Dawson's family moved to River Falls when he was five years old. While in high school he starred in both football and basketball, and was on the RFHS 1924 basketball team that went to the state tournament. He has the distinction of playing every minute of every game during the 1922 football season. Dawson was also a founder and the first President of the "R" Club which was formed during his senior year in 1924.
Dawson attended college in River Falls where he played both football and basketball, and was a member of three conference championships teams. After graduating from college he taught school for seven years in Elcho, WI before starting his 32 year tenure back in River Falls. He started as a teacher and eventually moved into administration. During World War II, when there was a shortage of male teachers, he took on the additional job of coaching the high school football team and was always one of the most fervent backers of high school and college sports. His football teams won conference titles in 1943 and 1945. He also coached the RFHS Boxing Team.
In the early years of his administration, Dawson served as the district Superintendent, Principal, Personell Director and Guidance Counselor, a job now split a dozen different ways. There was only one school building at the time, which served grades Kindergarten through grade twelve. During his tenure, Greenwood Elementary and a new Senior High School were built. The number of sports and activity offerings increased from just a handful to over 30 offerings when he retired.
In addition to sports Dawson enjoyed deer hunting and was an ardent fisherman, especially for trout on the Kinni. He refused to use a net to help land his fish. He felt that if he couldn't land it with his fishing rod alone, then he didn't deserve to have it.
The following was taken from an article written by former editor of the River Falls Journal, George Kramer:
"In school he was a somewhat strict taskmaster and was very dedicated in his work. It is impossible to tell exactly how many high school students he guided on to very successful careers, but the number has to be large. Students can recall with fond memories the "Lawrence Dawson" days at the school here. His legacy in the large number of those students who have had successful careers in teaching, in business, and in other fields of endeavor. I had the privilege of serving on the school board during the last two years before his retirement and can vouch for his efficient management of the affairs of the school district."