As always....***SPOILER ALERT***
I don't trust Lady Elizabeth Smallwood any farther than I can throw her. "I haven't done any of the things you're accusing me of," she tells Mycroft when he interrogates her in "The Six Thatchers." I did not like her word choice when I watched it the first time, chalking it up to shoddy writing, but then she flirts with him in "The Lying Detective."
Here is my theory. Lady Smallwood has been a double agent for years, but when she is finally confronted, Mycroft accuses her of a betrayal she did not commit. She is then able to say with complete honesty that she is innocent. However, she now knows that Mycroft is not above suspecting her of committing treason, and she, therefore, needs to keep Mycroft on her good side. What better way for her to do that than by using her feminine wiles? Smallwood will not succeed in seducing Mycroft, but it will succeed in distracting him. This will, no doubt, confuse Mycroft, and he will focus on her flirtatious behavior rather than her work with either Moriarty or Euros.