We introduce
λ-Reachability, a scalable approach to Hamilton--Jacobi safety analysis for high-dimensional robotic systems. Unlike prior discounted formulations that rely on fixed one-step Bellman updates,
λ-Reachability employs a stochastic multi-step estimator of the safety value, using a geometrically distributed rollout horizon together with a randomly absorbed terminal. Conceptually analogous to TD(
λ),
λ-Reachability interpolates between local self-consistency updates and long-horizon max-over-trajectory safety targets via an interpretable horizon-control parameter. Unlike TD(
λ), where the terminal value is always incorporated in learning targets, the terminal safety value in
λ-Reachability is only used at a probability controlled by parameter
δ. We formally show that for
δ<1, the update induces a contraction mapping that allows temporal-difference learning; as
λ→1, the estimator recovers the undiscounted reachability objective. We apply
λ-Reachability to high-dimensional safety learning problems with both simulated and real humanoid robots under balance and collision avoidance constraints. Experimental results demonstrate that
λ-Reachability significantly improves both safe-set boundary classification and safety margin estimation compared to single-step temporal-difference baselines.