Lysosomes are acidic organelles and are involved in various diseases, the most prominent is malaria. Accumulation of molecules in the cell by diffusion from the external solution into cytosol, lysosome and mitochondrium was calculated with the Fick-Nernst-Planck equation. The cell model considers the diffusion of neutral and ionic molecules across biomembranes, protonation to mono- or bivalent ions, adsorption to lipids, and electrical attraction or repulsion. Based on simulation results, high and selective accumulation in lysosomes was found for weak mono- and bivalent bases with intermediate to high log K (ow). These findings were validated with experimental results and by a comparison to the properties of antimalarial drugs in clinical use. For ten active compounds, nine were predicted to accumulate to a greater extent in lysosomes than in other organelles, six of these were in the optimum range predicted by the model and three were close. Five of the antimalarial drugs were lipophilic weak dibasic compounds. The predicted optimum properties for a selective accumulation of weak bivalent bases in lysosomes are consistent with experimental values and are more accurate than any prior calculation. This demonstrates that the cell model can be a useful tool for the design of effective lysosome-targeting drugs with minimal off-target interactions.