The former Cardiff City boss was placed in charge at Selhurst Park after Dougie Freedman left the club to join Bolton Wanderers, but despite guiding Palace to a 2-1 victory at Leicester City at the weekend, Lawrence has insisted that he will remain loyal to Freedman.
Lawrence said: "I have a loyalty to Dougie. I will not be applying for the full-time job.
"There has been interest from Bolton but I'm here and will do this job to the best of my ability."
Crystal Palace are currently in fourth place in the Championship table.