Previous works have considered the use of set invariance theory for fault detection and isolation in nonlinear Lure systems. This paper extends those results and proposes a new actuator fault-tolerant control approach. The fault-tolerant control scheme is designed based on linear parameter-varying (LPV) models of Lure systems. The actuator fault situation is diagnosed by an invariant set-based fault detection and isolation algorithm. Faults are compensated by adapting the controller gain based on estimates of the fault magnitude. Conditions for correct fault detection and isolation, and closed-loop stability are derived. The proposed fault-tolerant control scheme is compared with a linearised model approach and the performance of both, LPV-embedding and linearised, approaches are analysed for scalar and second-order systems. An example of a chaotic Chua circuit is also provided to illustrate the proposed fault-tolerant control scheme in higher-order systems.