Many realistic fluid flow problems are characterised by high Reynolds numbers and complex moving or deformable geometries. In our previous study, we presented a novel coupling between an iterative force-correction immersed boundary and a multi-domain cascaded lattice Boltzmann method, Falagkaris et al., and investigated flows around rigid bodies at Reynolds numbers up to 105. Here, we extend its application to flows around moving and deformable bodies with prescribed motions. Emphasis is given on the influence of the internal mass on the computation of the aerodynamic forces including deforming boundary applications where the rigid body approximation is no longer valid. Both the rigid body and the internal Lagrangian points approximations are examined. The resulting solver has been applied to viscous flows around an in-line oscillating cylinder, a pitching foil, a plunging SD7003 airfoil and a plunging and flapping NACA-0014 airfoil. Good agreement with experimental results and other numerical schemes has been obtained. It is shown that the internal Lagrangian points approximation accurately captures the internal mass effects in linear and angular motions, as well as in deforming motions, at Reynolds numbers up to 4 · 104. In all cases, the aerodynamic loads are significantly affected by the internal fluid forces.