Large Language Models (LLMs) increasingly leverage Federated Learning (FL) to utilize private, task-specific datasets for fine-tuning while preserving data privacy. However, while federated LLM frameworks effectively enable collaborative training without raw data sharing, they critically lack built-in mechanisms for regulatory compliance like GDPR's right to be forgotten. Integrating private data heightens concerns over data quality and long-term governance, yet existing distributed training frameworks offer no principled way to selectively remove specific client contributions post-training. Due to distributed data silos, stringent privacy constraints, and the intricacies of interdependent model aggregation, federated LLM unlearning is significantly more complex than centralized LLM unlearning. To address this gap, we introduce Oblivionis, a lightweight learning and unlearning framework that enables clients to selectively remove specific private data during federated LLM training, enhancing trustworthiness and regulatory compliance. By unifying FL and unlearning as a dual optimization objective, we incorporate 6 FL and 5 unlearning algorithms for comprehensive evaluation and comparative analysis, establishing a robust pipeline for federated LLM unlearning. Extensive experiments demonstrate that Oblivionis outperforms local training, achieving a robust balance between forgetting efficacy and model utility, with cross-algorithm comparisons providing clear directions for future LLM development.