Silicon-photonics-based optical neural network (ONN) is a promising hardware platform that could represent a paradigm shift in efficient AI with its CMOS-compatibility, flexibility, ultra-low execution latency, and high energy efficiency. In-situ training on the online programmable photonic chips is appealing but still encounters challenging issues in on-chip implementability, scalability, and efficiency. In this work, we propose a closed-loop ONN on-chip learning framework L2ight to enable scalable ONN mapping and efficient in-situ learning. L2ight adopts a three-stage learning flow that first calibrates the complicated photonic circuit states under challenging physical constraints, then performs photonic core mapping via combined analytical solving and zeroth-order optimization. A subspace learning procedure with multi-level sparsity is integrated into L2ight to enable in-situ gradient evaluation and fast adaptation, unleashing the power of optics for real on-chip intelligence. Extensive experiments demonstrate our proposed L2ight outperforms prior ONN training protocols with 3-order-of-magnitude higher scalability and over 30x better efficiency, when benchmarked on various models and learning tasks. This synergistic framework is the first scalable on-chip learning solution that pushes this emerging field from intractable to scalable and further to efficient for next-generation self-learnable photonic neural chips. From a co-design perspective, L2ight also provides essential insights for hardware-restricted unitary subspace optimization and efficient sparse training. We open-source our framework at the link.