"I do not have news. And you, Sarah?"
Translation:لَيْسَ عِنْدي أَخْبار وَأَنْتِ يا سارة؟
Yes, laisa ليس negates nominal sentences.
The sentence above is nominal. Here 3indii عندي is خبر "khabar" (the complement | predicate) of ليس laisa whereas 2akhbaar أخبار is مبتدأ مأخر "mubtada2 mu2akhkar" (the subject of the sentence, which is put after the complement).
Even though "3indii" عندي looks like in the genetive case, the phrase itself represents the nominative case, ie. as the خبر "khabar".