Zaydun al-ʿālimu: al-ʿālimu describes Zayd as an adjective.
Zaydun akhūka: akhūka is the intended badal.
In bi-l-nāṣiyati nāṣiyatin kādhibatin, both functions appear together: nāṣiyatin is badal, kādhibatin is its adjective.
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Badal or Adjective?
Badal: Definition, Four Types, and Parsing
Zaydun al-ʿālimu: al-ʿālimu describes Zayd as an adjective.
Zaydun akhūka: akhūka is the intended badal.
In bi-l-nāṣiyati nāṣiyatin kādhibatin, both functions appear together: nāṣiyatin is badal, kādhibatin is its adjective.