...for her letters to Kitty, though rather longer, were much too full of lines under the words to be made public. (Chapter 42)

I have always interpreted this reference to Lydia's letters to Kitty from Brighton differently than many who discuss them on these boards in that I do not imagine the letters contained any underscoring (which would be more difficult to do prolifically with a quill than it is with a ruler and ball point pen). Instead, I interpret the word lines to mean "lines of text;" so the passage might as well have read...

...for her letters to Kitty, though rather longer, were much too full of lines of private text under the lines of text to be shared with the family.

Dear Kitty,
Tell the family I went shopping yesterday, etc., etc.
Love,
Kitty
P.S. Yo, Kitty, just for you: Yesterday Wickham told me....