Laetitia was also the name of a Roman goddess or an epithet for the goddess Ceres. Wikipedia
Interestingly, there was also a St. Laetitia (or Leticia), supposedly a virgin martyr from Roman Britain, associated with St. Ursula as one of her companion martyrs. Wikipedia
According to the "The Penguin Dictionary of Saints" and " The Oxford Dictionary of Saints," the cult of St. Ursula (St. Laetitia supposedly being one of her fellow martyrs at Cologne ca. 4th Century) became popularized in the 12th century, in the wake of the discovery of a large number of bones (probably an old graveyard) in Cologne. Her legend was subsequently subject to wild elaboration, including, presumably, the addition of names for her companions. Since Ursula and her companions supposedly came from Roman Britain, that might be the origin of its popularity in the form of Lettice in England.
Thanks for the reference for the actual English name Lettice as a variant, rather than a nickname. Good to know. Like "Austin" for "Augustine."