The data-centric paradigm promoted by Industry 4.0 is accelerating Industrial Internet of Things (IIoT), resulting in increasingly frequent inter-departmental data interaction. Secure and efficient sharing therefore depends on reliable authentication among smart devices. Current schemes, however, do not jointly satisfy dynamic anonymity, traceability, and low overhead. Consequently, pseudonym management is cumbersome, revocation mechanisms are inflexible and costly. Therefore, we propose a Fibonacci-assisted lightweight anonymous revocable authentication (FLAR) scheme. By integrating a Fibonacci sequence with a hash chain, the scheme enables rapid signature verification. We design a dual parameter derivation algorithm to support swift pseudonym generation while maintaining data traceability and facilitating flexible revocation. Security is rigorously proven: existential unforgeability under chosen-message attacks (EU-CMA) is established in Random-Oracle Model (ROM), and Burrows-Abadi-Needham (BAN) logic plus ProVerif analyses confirm that all specified security properties hold. Performance evaluation shows that, FLAR markedly lowers than the other related schemes both computational and communication overhead, better fulfilling the lightweight and real-time demands of IIoT environments.