The deployment of large language models for specialized tasks often requires domain-specific parameter-efficient finetuning through Low-Rank Adaptation (LoRA) modules. However, effectively fusing these adapters to handle complex, multi-domain composite queries remains a critical challenge. Existing LoRA fusion approaches either use static weights, which assign equal relevance to each participating LoRA, or require data-intensive supervised training for every possible LoRA combination to obtain respective optimal fusion weights. We propose qa-FLoRA, a novel query-adaptive training-free method for LoRA fusion that dynamically computes layer-level fusion weights by measuring distributional divergence between the base model and respective adapters. Our approach eliminates the need for composite training data or domain-representative samples, making it readily applicable to existing adapter collections. Extensive experiments across nine multilingual composite tasks spanning mathematics, coding, and medical domains, show that qa-FLoRA outperforms static fusion by $\sim$5\% and training-free baselines by $\sim$7\%, while significantly closing the gap with supervised baselines. Further, layer-level analysis of our fusion weights reveals interpretable fusion patterns, demonstrating the effectiveness of our approach for robust multi-domain adaptation.