Secrecy is a motif in Sense and Sensibility which we find in two instances that stand out the most: first, when Edward Ferrars hides his engagement to Lucy Steele. Second, when Willoughby hides the real reason why he has to go to London and leaves Marianne in Barton, after having led her to believe that they were something more than just friends.
There are reasons why Edward hides his engagement from everybody: first, he may have come to realize that this engagement was too hasty and he now regrets it. Second, Lucy Steele is beneath Edward's social status and Edward's family is quite rich and snobby. Nevertheless, the secret, which is exposed by Lucy, herself, shocks Elinor in chapter 22:
(Elinor) It is strange, [...]that I should never have heard him even mention your name.
No; considering our situation, it was not strange. Our first care has been to keep the matter secret.-- You knew nothing of me, or my family, and, therefore, there could be no OCCASION for ever mentioning my name to you; and, as he was always particularly afraid of his sister's suspecting any thing, THAT was reason enough for his not mentioning it.
This engagement would later send Edward's mother into a frenzy. Edward is disowned by his mother after she finds out about it. In the end, Lucy Steele hides a little secret from Edward: her switch of affections, and her engagement, to Edward's brother, Robert. Karma catches up with Edward, in a big way.
As far as Willoughby goes, his lies can be found as early as chapter 16, when he suddenly takes off for London, leaving Marianne behind after quite the courtship. Elinor is the first to notice that his departure must be due to something more than Mrs. Smith's alleged summons for him to go to take care of "some businesses". Elinor clearly sees in Willoughby's demeanor that something else is going on. She openly says as much to her mother, much to her mother's disagreement:
...suspicion of something unpleasant is the inevitable consequence of such an alteration as we just witnessed in him. [...] Willoughby may undoubtedly have very sufficient reasons for his conduct, and I will hope that he has. But it would have been more like Willoughby to acknowledge them at once. Secrecy may be advisable; but still I cannot help wondering at its being practiced by him.
We later learn that Willoughby has been "promised" to a wealthy heiress in order to secure his financial future. After all, Willoughby is described as "independent", but not as rich. He confesses to his moderate means in different instances. However, his cruel abandonment of Marianne also comes with consequences: he is unhappy in his marriage, and he confesses to Elinor that his departure letter for Marianne was the idea of his then fiancee.
Therefore, secrets are catalysts that cause a chain of events for both Elinor and Marianne. However, the secrets are always exposed and Edward and Willoughby both pay for trying to hide their truths.