The increasing volume and complexity of Indian High Court judgments require high-quality automated summarization systems. Our agentic workflow framework for the summarization of Indian High Court judgments achieves competitive results without model fine-tuning. Experiments on CivilSum and IN-Abs test sets report ROUGE-1 F1 up to 0.547 and BERTScore F1 up to 0.866, comparable to state-of-the-art supervised models, with advantages in transparency and efficiency. We introduce two zero-shot modular agentic workflows: Lexical Modular Summarizer (LexA), a three-stage modular architecture optimized for lexical overlap (ROUGE), and Semantic Agentic Summarizer (SemA), a five-stage integrated architecture optimized for semantic similarity (BERTScore). Both workflows operate without supervised model fine-tuning, instead relying on strategic data processing, modular agent orchestration, and carefully engineered prompts. Our framework achieves ROUGE-1 F1 of 0.6326 and BERTScore F1 of 0.8902 on CivilSum test set, and ROUGE-1 F1 of 0.1951 and BERTScore F1 of 0.8299 on IN-Abs test set, substantially outperforming zero-shot baselines, rivaling leading fine-tuned transformer models while requiring no supervised training. This work demonstrates that modular, zero-shot agentic approaches can deliver production-grade results for legal summarization, offering a new direction for resource-limited judicial settings.