Federated learning (FL) over heterogeneous IoT edge devices faces coupled system-modality-data heterogeneity: the lower-cost device carries both fewer sensors and less computational power, so the slowest device (straggler) produces the most incomplete gradient signals. Naively averaging their updates dilutes rare-modality information and wastes computation on absent-sensor parameters, whereas existing methods handle the triple heterogeneity (system, modality, data) in isolation and none addresses their coupling. To resolve this issue, we propose RELIEF, a framework that partitions the fusion-layer Low-Rank Adaptation (LoRA) projection matrix into modality-aligned column blocks and uses this partition as a unified interface for aggregation, elastic training, and communication. Each block is aggregated only within the cohort of devices possessing that modality, which eliminates cross-modal gradient interference; the server then allocates personalized training budgets by prioritizing blocks with the highest cohort-internal divergence, so that resource-constrained devices train fewer but more impactful parameters. We prove that cohort-wise aggregation removes interference from the convergence bound and that the divergence-guided allocation achieves sublinear regret. Experiments on two IoT sensor datasets (PAMAP2, MHEALTH) under both full-parameter (CNN) and parameter-efficient (LoRA) training show that RELIEF achieves up to 9.41x speedup and 37% energy reduction over FedAvg with up to 15.3 pp rare-modality F1 gains, and real-device validation on a two-Jetson AGX Orin testbed confirms these results.

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