The two words "Ki" in this Pasuk seem to have different meanings!
Rashi and Rashbam: The first "Ki" in the Pasuk means 'because ("because she was afraid"), whereas the second one means 'but' ("but you did laugh"). In fact, 'Ki' has two other connotations
Riva: The Targum of [almost] every Ki is Arei, for Arei has these four meanings in Arama'ic.
Why did Sarah deny that she laughed even after Avraham had rebuked her, ostensibly in the name of Hashem?
Ramban: Avraham did not quote Hashem; so she thought that he was taking her to task off his own bat. Perhaps he had seen some giveaway sign on her face, or because she had failed to acknowledge the good news. The moment he said to her 'No, but you did laugh!', she realized that he had spoken prophetically and she stopped denying.
Who said "Lo Ki Tzachakt"?
Rashi and Targum Yonasan: The Mal'ach 1 (Micha'el) who spoke to her in Pasuk 14.
Seforno: Avraham, who knew that if Hashem said that she laughed, then she laughed.
See Na'ar Yonasan, who cites Chazal that it was Hashem who spoke directly to Sarah
What did the angel mean when he said "Lo ... "?
Rashi: "Lo Ki" means 'but'. 1
Targum Onkelos: 'No, but you did laugh!'
Targum Yonasan: 'Don't be afraid!' 2
Why does it say "and Sarah denied" (and not that she said)?
Hadar Zekenim: This shows that women deny.