لِأَقْتَبِسَ مِنْ فَوَائِدِهِ
So that I might take something useful from his insights.
Aqtabisa originally suggests taking a flame or light from a fire. Used of knowledge, it means to acquire an insight or benefit. Fawāʾid are useful points.
The initial li- marks purpose: this is why he moved nearer.