طَلَبًا لِلْعِلْمِ: ṭalaban is an accusative reason complement; al-ʿilmi is genitive after lām.
لِطَلَبِ الْعِلْمِ: ṭalabi is genitive after lām, and al-ʿilmi is its genitive iḍāfa complement.
Similar meaning does not imply identical parsing.
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Why the Case Changes with Lām
Al-Mafʿūl Lahu: Expressing the Reason for an Action
طَلَبًا لِلْعِلْمِ: ṭalaban is an accusative reason complement; al-ʿilmi is genitive after lām.
لِطَلَبِ الْعِلْمِ: ṭalabi is genitive after lām, and al-ʿilmi is its genitive iḍāfa complement.
Similar meaning does not imply identical parsing.