Foundation models (FMs) have shown remarkable advancements in enhancing the performance of intelligent applications. To address the need for data privacy in FM fine-tuning, federated learning has emerged as the de facto framework. Specifically, Federated FMs (FedFMs) fine-tuning using low-rank adaptation (LoRA) modules instead of the full model over multiple clients can achieve both parameter efficiency and data privacy. However, recent studies rarely address the challenges posed by clients with heterogeneous resources, particularly in GPU memory capacity. In this paper, we introduce Fed-piLot, an efficient FedFM fine-tuning framework with optimized local LoRA assignments for heterogeneous clients. By emphasizing the different memory consumption for training different LoRA layers, as well as the varying contributions of different layers to model performance, we formulate the LoRA assignment as a Knapsack Optimization Problem. We design a Local-Global Information Gain Score (IG-Score) based value function to optimize LoRA assignment under clients' memory constraints. To further mitigate the impact of heterogeneity in model updates, we propose a novel Spatial-Temporal model aggregation (STAgg) rule using the Dynamic Weight Adjustment (DWA) strategy. Experimental results on three datasets under both IID and non-IID conditions demonstrate the effectiveness and efficiency of Fed-piLot. The code will be publicly available.