Federated Learning (FL) typically involves a large-scale, distributed system with individual user devices/servers training models locally and then aggregating their model updates on a trusted central server. Existing systems for FL often use an always-on server for model aggregation, which can be inefficient in terms of resource utilization. They also may be inelastic in their resource management. This is particularly exacerbated when aggregating model updates at scale in a highly dynamic environment with varying numbers of heterogeneous user devices/servers. We present LIFL, a lightweight and elastic serverless cloud platform with fine-grained resource management for efficient FL aggregation at scale. LIFL is enhanced by a streamlined, event-driven serverless design that eliminates the individual, heavyweight message broker and replaces inefficient container-based sidecars with lightweight eBPF-based proxies. We leverage shared memory processing to achieve high-performance communication for hierarchical aggregation, which is commonly adopted to speed up FL aggregation at scale. We further introduce the locality-aware placement in LIFL to maximize the benefits of shared memory processing. LIFL precisely scales and carefully reuses the resources for hierarchical aggregation to achieve the highest degree of parallelism, while minimizing aggregation time and resource consumption. Our preliminary experimental results show that LIFL achieves significant improvement in resource efficiency and aggregation speed for supporting FL at scale, compared to existing serverful and serverless FL systems.