Data lakehouses run sensitive workloads, where AI-driven automation raises concerns about trust, correctness, and governance. We argue that API-first, programmable lakehouses provide the right abstractions for safe-by-design, agentic workflows. Using Bauplan as a case study, we show how data branching and declarative environments extend naturally to agents, enabling reproducibility and observability while reducing the attack surface. We present a proof-of-concept in which agents repair data pipelines using correctness checks inspired by proof-carrying code. Our prototype demonstrates that untrusted AI agents can operate safely on production data and outlines a path toward a fully agentic lakehouse.