Her teacher was always warning her against using too much italics.

I personally interpret "too full of lines under the words" as, literally, underlined words followed by many an exclamation point.

Though it is possible that, at the time, some people might have used various techniques to convey secret meanings in their letters, I think Lydia is quite simply too stupid to use them. (and Kitty to understand what Lydia would write to her)