What you are looking at

The dashed blue curve is the linearised growth: a tangent vector evolved with the variational equation, which grows exponentially forever because nothing constrains it. The orange curve is the real separation between two trajectories seeded δ apart — identical to the linear estimate while δ stays small, then saturating at the size of the attractor, because two points on a bounded set can only get so far apart. The slope of the straight section is λ.

λ converges slowly. At t_max = 40 expect roughly 0.79 for the classic parameters; push t_max up and it climbs toward the accepted 0.906. That drift is a property of finite-time Lyapunov exponents, not of the solver.

Truncation error is amplified at the same rate as any physical perturbation, so below δ ≈ 1e-6 the divergence is arithmetic rather than dynamics. Enable the noise-floor control to integrate a third time at rtol=1e-11 and plot that error alongside.