Individualized instruction is a type of educational principle. On the one hand, it necessitates the creation of individualized teaching resources, courses, and methods. Students, on the other hand, require a high level of autonomy and the ability to make personalized plans based on their own cognitive characteristics and needs. The big data (BD) era opens up new possibilities for IE (ideological education) work in universities, but it also poses some challenges. IE development will be greatly aided by recognizing opportunities to meet challenges and optimizing and integrating PL (political lesson) resources. The LNN (Lagrange neural network) model has been established. The simulation results show that the LNN network can converge to the optimal solution quickly and effectively and then reconstruct sparse signals. Individualized college PL instruction using LNN and BD technology helps students communicate more effectively and improves the pertinence, immediacy, and positivity of IE.