Federated sequential recommendation (FedSeqRec) aims to perform next-item prediction while keeping user data decentralised, yet model quality is frequently constrained by fragmented, noisy, and homogeneous interaction logs stored on individual devices. Many existing approaches attempt to compensate through manual data augmentation or additional server-side constraints, but these strategies either introduce limited semantic diversity or increase system overhead. To overcome these challenges, we propose \textbf{LUMOS}, a parameter-isolated FedSeqRec architecture that integrates large language models (LLMs) as \emph{local semantic generators}. Instead of sharing gradients or auxiliary parameters, LUMOS privately invokes an on-device LLM to construct three complementary sequence variants from each user history: (i) \emph{future-oriented} trajectories that infer plausible behavioural continuations, (ii) \emph{semantically equivalent rephrasings} that retain user intent while diversifying interaction patterns, and (iii) \emph{preference-inconsistent counterfactuals} that serve as informative negatives. These synthesized sequences are jointly encoded within the federated backbone through a tri-view contrastive optimisation scheme, enabling richer representation learning without exposing sensitive information. Experimental results across three public benchmarks show that LUMOS achieves consistent gains over competitive centralised and federated baselines on HR@20 and NDCG@20. In addition, the use of semantically grounded positive signals and counterfactual negatives improves robustness under noisy and adversarial environments, even without dedicated server-side protection modules. Overall, this work demonstrates the potential of LLM-driven semantic generation as a new paradigm for advancing privacy-preserving federated recommendation.