LLMs are increasingly deployed in autonomous laboratories, under the assumption that their domain priors and reasoning over iterative feedback let them converge on good designs in fewer iterations than feedback-only baselines. Current iterative scientific design benchmarks, however, score only outcome snapshots at fixed horizons. This leaves the learning trajectory unmeasured, even though the trajectory is what captures learning efficiency, where each iteration saved is a real saving in cost and time. Motivated by this, we examine three evaluation choices that change the conclusions one draws about LLM learning efficiency in iterative scientific design: what to measure, what baseline to compare against, and what to ground against. We introduce LEAPBench, Learning Efficiency in Adaptive Processes, a 55-task framework that pairs a best-so-far area under the curve (AUC) trajectory metric with a classical Bayesian-optimization reference and an audit grounded in published literature. Applied to eight contemporary LLMs, switching from final-outcome to trajectory scoring changes the best-model decision on 53% of tasks at matched horizons, and exposes efficiency gains overlooked by outcome-based scoring. LLMs do not outperform a classical Bayesian baseline. On 16 biology tasks where the oracle's reward signal is aligned with configurations from the published-best design, domain-aware prompting leads to LLM choices that match the published-best's approximately 10 percentage points less often than domain-agnostic prompting at iteration 30. The pattern is sharpest on 6 tasks where the literature-typical and published-best configurations diverge, and domain-agnostic prompting matches the published-best more often on all 6. The trajectory metric also doubles as a tractable training target. Offline reinforcement learning with the metric as a reward improves performance on 14 of 21 held-out tasks.