Relative alchemical binding free energy calculations can be used to predict the effect of amino acid mutations on ligand binding affinities. However, these protocols are not well established for proteins containing intrinsically disordered regions (IDRs). In this work, we focus on the development of robust protein-free energy perturbation (FEP) protocols to reproduce experimental binding affinities that have been measured for a panel of mutants of the protein MDM2 against two ligands, AM-7209 and Nutlin-3a. We focus on mutations that occur in the N-terminal IDR lid of MDM2, which is known to undergo ligand-dependent folding upon binding. We systematically assess the effectiveness of both equilibrium and nonequilibrium alchemical protocols in reproducing these experimental binding affinities, in particular for mutations with slowly varying degrees of freedom. We show that the equilibrium protocol outperforms the nonequilibrium protocol in the precision of the free energy estimates obtained. In addition, we demonstrate the effect of the protein force field and the water model used to simulate the highly flexible IDR region. Overall, our findings demonstrate an accurate FEP protocol capable of reproducing these trends and further show the applicability of FEP protocols for elucidating the mutational effects on ligand binding affinity in highly dynamic intrinsically disordered protein regions.