Federated parameter-efficient fine-tuning enables clients to adapt pre-trained models without sharing raw data or communicating the full model, but statistical heterogeneity makes a single global adapter insufficient for personalized prediction. Existing personalized methods typically use the same low-rank structure for both shared and private adaptation, overlooking their distinct requirements for aggregation and personalization. We propose FedLAFP, a role-aware framework that couples a compact, globally aggregated LoRA branch with a client-private, full-rank-capable RandLoRA branch. The shared branch provides an efficient interface for transferring common knowledge, whereas the private branch combines fixed random low-rank bases with learned scaling coefficients to provide expressive client-specific adaptation without additional communication. Client- and layer-specific mixing coefficients jointly fuse the two branches, and only the shared LoRA parameters are exchanged. A controlled linear study supports this role assignment: LoRA yields more aligned client updates and lower aggregation error, while RandLoRA more accurately recovers client-specific residuals. Experiments across four visual recognition benchmarks show that FedLAFP consistently outperforms local-only and federated LoRA baselines, achieving an average personalized accuracy of $86.93\%$ and exceeding the best baseline average by $1.30$ percentage points.

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