•Implementation of LBM framework with domain transferring is disclosed.•It allows for particle settling simulations in virtually unbounded domain.•Memory demand may be reduced by an order of magnitude for IBM simulations.•With IBM, a detailed meshing procedure is described for ellipsoidal particles.•Very good agreement was found against experimental and independent CFD results. Particle settling at moderate to high Reynolds number takes a considerable distance to reach a periodical or statistically steady regime. Hence, hardware memory limitations in fully resolved simulations constrain the maximum domain size for this flow class. Due to the locality in most of its algorithms, the Lattice Boltzmann Method (LBM) is increasingly popular for CFD studies. In the present paper, a domain transferring scheme is implemented in LBM, enabling simulations of particle motion in a virtually infinite domain, and it is combined with a high-quality Lagrangian mesh algorithm to be solved with the Immersed Boundary Method (IBM). A thorough mesh generation procedure for ellipsoidal particles is disclosed, as well as an extension of the internal mass compensation strategy of Suzuki and Inamuro (2011). Comparison with analytical results shows that the numerical model appropriately describes the particle rotation and can predict a terminal velocity close to Stokes solution. The numerical results of a buoyant sphere moving diagonally presented remarkable concordance with experimental data. Also, an excellent agreement with a numerical study of oblate spheroids settling in a vast domain was found. The domain transferring scheme reduced the memory demand in one order of magnitude.