The reason why the character of Lise in the story "The Ring" keeps the incident in the glade a secret from her husband is because she knows that she has committed an indiscretion, either physically or mentally.
This indiscretion could be interpreted either as an actual sexual encounter with another man, or the want of being taken by the thief that she found in the woods. We know that there is more to Lise than what the story shows. If we read between the lines we find a side of Lisa that is curious about the evils of the world. Lise has been living in a form of fish tank in which she has been hidden from the horrors of life. To find an actual "sinner" would be a very curious and enticing experience even for her. Moreover, she gives up her ring to the thief so that he would not kill her. She does not battle for it, nor does she try to protect it. Conversely, she is more than quick when she chooses it as her bargaining piece.
Therefore, Lise has sinned, in her heart. She has noted that this marriage that she gloats about is not the ideal that she dreams of. She wants to be wanted, loved, and served. She also wants to command, take action, and taste life. This is her biggest problem: She is not in the right time nor place to experience these sensations and, what's worse, she is already married, living in isolation, and below her typical means.