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Generating a class integration test order (CITO) is essential to reduce the overhead of test stub construction (the primary cost in integration testing) and to ensure system reliability in complex software systems. Although reinforcement learning (RL) has shown promise in automating CITO generation, existing methods suffer from unstable policy learning and limited robustness against structural perturbations and defect injection. These challenges stem from insufficient reward shaping and the lack of reliable oracles for validation. To address these limitations, we propose LM-CITO, a stability-aware RL framework that integrates Lyapunov-guided reward shaping with semantic validation through metamorphic testing (MT). Specifically, we design a Lyapunov energy function over class dependency graphs to promote monotonic structural convergence during training, and define metamorphic relations (MRs) to verify behavioral consistency under controlled perturbations. Extensive experiments on six real-world systems demonstrate that LM-CITO consistently produces more effective policies, yielding CITOs with significantly reduced stubbing costs compared to baseline models. Furthermore, MT verifies the capability of our MRs to detect defects in 19 injected bug variants, confirming the robustness of LM-CITO under various fault-induced perturbations. These results highlight the synergy of stability guidance and MR-based validation, offering an effective, principled solution for oracle-free RL in software testing.