AI agents are increasingly the primary consumers of data, operating continuously to make concurrent, irreversible decisions. Traditional data systems designed for human analysis cycles become correctness bottlenecks under this operating regime. When multiple agents operate over shared resources, their actions interact before reconciliation is possible. Correctness guarantees that apply after the decision window therefore fail to prevent conflicts. We introduce the Decision Coherence Law: for agents that take irreversible actions whose effects interact, correctness requires that interacting decisions be evaluated against a coherent representation of reality at the moment they are made. We show that no existing system class satisfies this requirement and prove through the Composition Impossibility Theorem that independently advancing systems cannot be composed to provide Decision Coherence while preserving their native system classes. From this impossibility result, we derive Context Lake as a necessary system class with three requirements: (1) semantic operations as native capabilities, (2) transactional consistency over all decision-relevant state, and (3) operational envelopes bounding staleness and degradation under load. We formalize the architectural invariants, enforcement boundaries, and admissibility conditions required for correctness in collective agent systems. This position paper establishes the theoretical foundation for Context Lakes, identifies why existing architectures fail, and specifies what systems must guarantee for AI agents to operate constructively at scale.