Transforming relational databases into knowledge graphs with enriched ontologies enhances semantic interoperability and unlocks advanced graph-based learning and reasoning over data. However, previous approaches either demand significant manual effort to derive an ontology from a database schema or produce only a basic ontology. We present RIGOR, Retrieval-augmented Iterative Generation of RDB Ontologies, an LLM-driven approach that turns relational schemas into rich OWL ontologies with minimal human effort. RIGOR combines three sources via RAG, the database schema and its documentation, a repository of domain ontologies, and a growing core ontology, to prompt a generative LLM for producing successive, provenance-tagged delta ontology fragments. Each fragment is refined by a judge-LLM before being merged into the core ontology, and the process iterates table-by-table following foreign key constraints until coverage is complete. Applied to real-world databases, our approach outputs ontologies that score highly on standard quality dimensions such as accuracy, completeness, conciseness, adaptability, clarity, and consistency, while substantially reducing manual effort.