His parents were Lucy Tracy and Campbell Dickson, who worked as a banker. Campbell was also a merchant and made money through investing in real estate. Leonard attended both primary and secondary school in his home town of Cleburne.
Ang kanyang mga magulang ay Lucy Tracy at Campbell Dickson, na nagtrabaho bilang isang bangkero. Campbell ay din ng isang merchant at ginawa ng pera sa pamamagitan ng pamumuhunan sa real estate. Leonard pumasok sa parehong primarya at sekundaryong mga paaralan sa kanyang sariling bayan ng Cleburne.