"Lita" is a lot like "Tina" -- it has a number of possible origins, as it was originally a nickname. So, as "Tina" could come from Christina, Clementina, Martina, etc., "Lita" could be from any of a number of names -- including Lolita, Angelita, Carmelita, Manuelita and Perlita. If your name came from a particular source (i.e. your Aunt Adelita), then you can trace it back to that source name and figure out the meaning. Otherwise, the meaning is ambiguous.
"Jan" -- be it from Jane, Janet, Janice, John, Johannes, or any other related name -- can be traced back to a Hebrew name meaning "God is gracious." So the meaning is definitely God-related.
But "Kara" is like "Lita" in that its meaning depends on the specific source. If it's related to Katherine, then the meaning might be "pure" (though the meaning of Katherine is itself debated). If it's from Caroline, it can be traced to Charles, which means "man." If it's simply from Cara, it could be either "face" or "expensive" in Spanish, "friend" in Irish, or "beloved" in Italian (i.e., "cara mia" = "my beloved"). And "Kara," being such a simple word, probably also appears in a number of other languages, and therefore probably has many other possible meanings.
If you can give me some specifics on where Lita and Kara came from, I might be able to be a bit more helpful.