In the present work, we investigate the accuracy and robustness of our in-house OpenMP parallelized direct-forcing immersed boundary–lattice Boltzmann (DF-IB-LB) solver by undertaking studies on accuracy, discrete conservation, Galilean invariance and quantification of spurious force oscillations (SFO). Our study reveals that DF-IB-LB exhibits first and second-order spatial accuracy for velocity and pressure errors, respectively, for generic moving boundary problems. The method is found to be Galilean invariant, while errors in discrete conservation and SFO decay linearly and superlinearly, respectively, with grid refinement. The numerical simulations with the proposed solver on a vast number of complex moving boundary problems involving imposed and induced motion highlight its efficacy as a fast, robust and accurate framework for single-phase flows with and without fluid–particle interactions. © 2022, The Author(s) under exclusive licence to OWZ.