Paul's two caveats in 1 Cor 9:20-21: not under the Law of Moses, but also not lawless — under the law of Christ

When with Jews, Paul clarifies he is not himself under the law. When with Gentiles, he clarifies he is not without law before God but is "under the law of Christ." This is Paul's fulfillment-theology framework: the Law of Moses is fulfilled in Christ; Christians are not lawless but are under a new (higher) framework — the law of Christ.