One easy way to get Letty as a nickname is Violetta. Violetta (vee-oh-let-ta) is a more elegant, romantic and European version of the trending and popular Violet, and while both of them mean "purple/violet," it is a very distinct shade of purple they refer to - the shade violet, as in the flower. It is of Latin origin but used in several countries.
One of the most well known namesakes of Violetta is from Giuseppe Verdi's opera "La Traviata," which was originally titled "Violetta" after the main character. The story in the play was adapted from Alexandre Dumas junior's novel The Lady of the Camellias. (Side note: I had no idea Alexandre Dumas was part Afro-Carribean Creole until I saw "Django Unchained.") In the opera, Violetta is a respected courtesan who abandons her lifestyle when she falls in love with a man named Alfredo. A few events and misunderstandings unfold, Violetta breaks off their relationship, and... well, I won't ruin the ending for you. But I kind of love this play and Violetta's character, because even though she is a courtesan, she is highly respected and loved.
I once read that there was a Saint Violetta of Verona, Italy, but cannot find any record of her. Something about a Persian violet. Who knows.
What's shocking is that Violetta only ranked once - in 1884 at #849. In recent years it has been very rare. 46 girls were given the name in 2011, and no more than 30 since 1884. In most years it was given between 5 and 20 times.