The correct options are
A Let the chips fall where they may
D Let it go with the wind
In the given conversation: Lyle says, "I don't mind''. This means that she does not worry about the result of telling Fenny about her shoddy work. The expression, 'Let the chips fall where they may' means 'To allow events to unfold naturally and to accept what occurs without prejudice, worry, or regret'. Hence, this expression meaningfully completes the sentence and option A is correct.
Option B: 'Go with the wind' means 'to just let things happen as they do, whether they're planned or come out of nowhere'. This expression is also appropriate and meaningfully completes the sentence. Hence, option B is also correct.
Option C: 'Two-timing' means 'to deceive or be unfaithful to a lover or spouse'. It is normally expected that one would be faithful to one's lover or spouse and not have an affair with another person at the same time. However, if one does so, it is called 'two-timing'.
Option D: 'I'm going to hit the sack' means 'I am tired and going to bed'.
Given the meanings as above, these expressions cannot be used to complete the given conversation meaningfully. Hence, options C and D are incorrect.