LaQuincey was born in Lawton, Oklahoma to military family. His family lived in several states until his family returned to Lawton. He graduated from the University of Oklahoma in 2005 with a BFA in studio art. After graduating he assisted Paul Moore on the Oklahoma Land Run Monument. He assisted with sculpting various elements of the monument and made molds for the monument. In his own work, LaQuincey has completed several commissions for universities in Oklahoma. He has a life-size bronze sculpture of past president James R. Scales and bison reliefs installed on the campus of Oklahoma Baptist University in Shawnee, Oklahoma. The Fred Jones Junior Museum of Art's Eugene Adkins wing at the University of Oklahoma in Norman, Oklahoma has a portrait bust of Eugene Adkins by LaQuincey in their collection.