Cell migration plays a critical role in various biological processes, including cancer cell metastasis. This phenomenon is inherently complex and involves interactions between the deformable cell body and the surrounding fluid. Because cell migration occurs at extremely small flow speeds and spatial scales, the associated Reynolds numbers are very low. In that case, the standard explicit lattice Boltzmann–immersed boundary (LB-IB) method reaches steady state very slowly, making it inefficient and computationally expensive for modeling cell migration. To overcome this limitation, we propose an implicit lattice Boltzmann–immersed boundary method based on solving the stationary Stokes equations. The approach consists of three main steps: first, we linearize the original LB-IB mathematical formulation; second, we recast the linearized formulation into a large, sparse system of algebraic equations (Ax = b); and finally, we solve this system using iterative methods such as the Generalized Minimum Residual (GMRES) method with suitable preconditioners. We have applied this framework to simulate the relaxation of a perturbed cell toward its equilibrium state within a two-dimensional viscous incompressible fluid. Preliminary results indicate that the linearized LB-IB method maintains acceptable accuracy relative to the original explicit version while significantly reducing computation time. Our current work focuses on numerical solutions of the large sparse linear systems that arise in this framework.