More and more lunar exploration missions require robots that can adapt to the complex and unpredictable terrain of the lunar surface, where the low gravity makes quadrupedal jumping an efficient mode of movement. However, the prolonged flight phase resulting from this one-sixth Earth gravity, combined with other unchanged inertial forces, amplifies the rotational effects caused by suboptimal jumping actions and the resulting angular momentum in intricate terrains. To address the limitations of existing models in understanding the long-term consequences of sequential behavior, this paper proposes a Transformer-based reinforcement learning algorithm with causal sequence inputs to enhance jumping adaptation in complex lunar environments. A customized feature extractor for sequence input streams is designed and integrated into a reinforcement learning policy head equipped with a Transformer attention mechanism, employing a temporal window to maintain both temporal continuity and sampling randomness. Additionally, a stepwise curriculum learning framework building on the jumping and stabilization skills acquired on a plane ground is implemented, transferring to various levels of randomized rugged terrains and lunar pits of different sizes with irregular edges. This approach avoids conservative strategies and enhances training efficiency. The proposed algorithm successfully achieves efficient jumping in complex simulated lunar tasks and demonstrates superior performance compared to ablation groups across various metrics.