Fibrous filter media are made of small fibers (micro and nanoscale). In these cases, the Knudsen number can be appreciable and the slip phenomenon on the fluid boundary surfaces should be considered. For this purpose, the mesoscopic approach lattice Boltzmann method (LBM) can be applied to predict the flow, with appropriate boundary conditions (BC). This paper analyzes a fibrous microfilter, including the construction of the geometric model from scanning electron microscope (SEM) images, and the comparison with experimental results and macroscopic approach modeling. A slip condition was implemented in open-source code OpenLB, based on specular reflections of the populations. The validation of the proposed boundary condition was carried out by simulations in a 2D channel, disposed at 45 and 90 degrees, and simple cases of a flow around an octagon. The experimental order of convergence (EOC) was evaluated for all cases and the results of the pressure drop around the octagon were compared to data obtained by a macroscopic approach. A good agreement between the pressure drop through the filter media and the results obtained numerically and experimentally was observed. These findings endorse the accuracy of the implemented slip BC and the importance in considering this phenomenon in microscale systems.