No. There is no magic involved. The series has not been consistent in what criteria must be met to be a Time Lord. Some stories have suggested it is a title earned through study ("The Deadly Assassin", etc.) while more recently Time Lord has been depicted as a species with its own unique DNA that developed due to billions of years of exposure to the untempered schism of the time vortex, as indicated in "A Good Man Goes to War", though earlier episodes such as "The Doctor's Daughter" had already established Time Lord as a species.