Bear in mind that the name 'Lettice' predates the common use of the word 'lettuce' and was a common Medieval name when salad vegetables, being under the dominion of whichever planet was cold wet and nasty [Mercury? I never was up on astrology] were considered dangerous to eat, and were just known as 'sallet' or lumped in with 'worts', or vegetables. It was latinised to Laeticia, which became used in its own right when literacy was sufficiently widespread for people to see it written. The pet name for it was Lecia, later also Letty. The later form 'Letitia' had the shortening 'Titty' and was used for a character in Arthur Ransome's 'Swallows and Amaons' series when said shortening was less smutty than it is now. Modern usage also comes up with names with even more apparent double meaning - look at Randy which is even spelled like its meaning of 'sex-mad' having become separated from its proper source, 'Randolph' Names, even those from Western roots, come to us from a wide variety of sources, from as far away as Ancient Greece and Byantium to those as ancient as Etruscan, Gothic and Celtic. Some have changed on the way; few men called Lewis are aware that their name started out as Clovis, and went variously through Ludovic by one route and Aloysius [Allo-ISH-us] by another. Lettice is old fashioned, but pops up occasionally, usually in the aristocracy where it may be a traditional name in some families, such as those descended from Lettice Knollys, like the Spencer-Churchills.
Names, even those from Western roots, come to us from a wide variety of sources, from as far away as Ancient Greece and Byantium to those as ancient as Etruscan, Gothic and Celtic. Some have changed on the way; few men called Lewis are aware that their name started out as Clovis, and went variously through Ludovic by one route and Aloysius [Allo-ISH-us] by another. Lettice is old fashioned, but pops up occasionally, usually in the aristocracy where it may be a traditional name in some families, such as those descended from Lettice Knollys, like the Spencer-Churchills.