Lettice /let-tice/ [2 sylls.] as a name for girls is of Latin origin, and the name Lettice means joy.Lettice is an alternate form of Letitia (Latin): Latin version of the name. Compare last name Lettis. Kreatif forms: Leitice, Lettire, Lotice.2000 U.S. Census). Shown below is a comparison of the usage of Lettice and related names. Prominent varying forms of Lettice (not ranked) ranked in the Top 1000 are Letta, Lettie, Tisha, Letitia, Leticia, Leda, Leta, Letha and Latisha.