In «جَاءَ الْقَوْمُ لَيْسَ زَيْدًا» and «جَاءَ الْقَوْمُ لَا يَكُونُ زَيْدًا», Zaydan is accusative as the predicate of the defective verb.
Laysa is a defective verb; its subject is an understood pronoun in this analysis, while Zaydan is its accusative predicate.
Do not attribute its case directly to the particle illā, which is absent here.