The correct answer is C. for.
Slander is a false statement of fact that is harmful to a person’s reputation. If you persist in telling lies to me, I will sue you for slander. This means that I will file a lawsuit against you, asking the court to order you to stop telling lies about me and to pay me damages for the harm that your lies have caused me.
The other options are incorrect because they do not make sense in the context of the sentence. Option A, “to,” would make sense if I was asking you to do something, such as “I shall sue you to stop telling lies to me.” Option B, “on,” would make sense if I was blaming you for something, such as “I shall sue you on the grounds of slander.” Option D, “with,” would make sense if I was using something, such as “I shall sue you with the evidence of your lies.”
I hope this explanation is helpful. Please let me know if you have any other questions.