Ok, since nobody else has said it...
Don't use String™. It can cause hangs and crashes at random times, especially when your program runs for a long time, or when you add features to your program. You don't even use String methods on those constants. Simply change the languages array declaration to this:
const char *languages[] = {"Kalba?", "Language?", "Runa?", "Yazyk?"};
The LCD print doesn't have to change. It can print char *, too:
lcd.print(languages[langCycle]);
Arrays of characters are much more efficient than using the String class. They are also called "C strings" (note the lowercase "string").
If you have questions about how to do something with C strings, just ask. There are many C string functions to choose from. The complete list of functions is here, and some tutorials are here and here. Good alternative reference here.