The story has turned into a whodunit. Why is lady Dedlock suspected of murdering Mr. Tulkinghorn?

Tulkinghorn had already assured Lady Dedlock that he planned to reveal her secret about having borne Hawdon's child, but that he would do it in his own time. Thisi s a huge threat to her, since it will not only ruin her but will hurt Sir Leicester greatly. She was walking outside the night Tulkinghorn is murdered, and is a likely suspect.