Okay, so one day a timelord called 'The Doctor' returned to his home planet Gallifrey and brought with him a friend, Leela, a human of the tribe of the Sevateem, who were descended from Earth humans. Leela fell in love with one of the timelords she met on Gallifrey. She stayed there and raised a family which included a son, half human and half timelord, whom she named 'The Doctor' after the timelord who brought her to Gallifrey.
Leela's son, The Doctor grew up and, in time, became a father himself. The Doctor's son was one quarter human and called himself 'The Master'. He was determined to rule Gallifrey and then the multiverse. The Master had a daughter called Susan (after Susan Maugham, a singer from Earth who The master was a bit keen on). Susan was one eighth human and seven eighths timelord.
The Master was an abusive parent, physically and mentally. Susan's Grandfather, The Doctor, had to get her away from her father to somewhere safe. While The Master was preoccupied trying to conquer Gallifrey The Doctor and Susan hotwired an old Type 40 Tardis and went to Earth in the early 1960s (Susan had always wanted to go because it was the era of her namesake).
The Master was defeated by the other timelords and went off to plot and plan again. Eventually The Master and The Doctor would cross swords again but The Master never traced where Susan was hiding. The Doctor had used timelord trickery to mask her presence from all detection, even his own.
Susan eventually became a mother and her children were all one 16th timelord and thus the timelord gene became part of the human genome and thus was already present in Leela even when The Doctor first met her on the planet colonised by the Sevateem.