Cell processing applications, including hydrodynamic cell separation in microfluidic systems, benefit from accurate modelling of deformable particles in flow to optimise processes and equipment. Understanding how biomarkers, such as ATP concentration, influence membrane mechanics and deformability is also advantageous for reducing cell waste and improving personalised therapy design. Computational fluid dynamics (CFD) can directly support the characterisation of cells; however, simulations of individual cells remain computationally demanding due to strong fluid-structure interaction and interfacial coupling, and robust numerical frameworks are required to capture cell deformability under realistic flow conditions. In this work, a GPU-accelerated multiphase lattice Boltzmann-immersed boundary method (LBM-IBM) CFD software tool is presented for the simulation of deformable cells subject to hydrodynamic and externally applied body forces. The solver is coupled with a state-of-the-art spring-network red blood cell model and supports viscosity ratios between the suspending fluid and cytosol, multiple cell morphologies, and the application of forces through LBM boundary conditions and IBM modifications. Discocyte and echinocyte-II cells are simulated in flow with verification and validation against benchmark cases, including optical tweezers, shear flow, and sedimentation due to gravitational and magnetic forces, with echinocyte-II cells simulated in flow, to the authors’ knowledge, for the first time. Results demonstrate robust fluid-structure coupling across multiple forcing regimes and highlight deformation-dependent transient velocity responses relevant to non-chemical microfluidic cell separation strategies. In terms of efficiency, the solver demonstrates comparable performance to solvers in the literature, with an extended million lattice updates per second (MLUPS) metric incorporating fluid-structure interactions proposed to better quantify efficiency for multiphase in-flow cell simulations. The framework provides a unified computational approach for multiphase particle simulations, enabling the investigation of transport phenomena relevant to biofluid engineering applications. Future extensions incorporating additional gas phases and multispecies transport are planned to expand the multiphysics capabilities of the solver.