Available observational data regarding current cosmological characteristics suggest that the universe is, to a large extent, both isotropic and homogeneous on a large scale. In this study, our objective is to analyze the Friedmann-Lemaitre-Robertson-Walker (FLRW) space-time using a perfect fluid distribution. We specifically investigate the framework of f(R, Lm) gravity within certain constraints. To accomplish this, we concentrate on a specific nonlinear f(R, Lm) model, represented by f(R, Lm) = R/2 + Lαm. The field equations are solved using the equation of state parameter of the form of the Chevallier-Polarski-Linder (CPL) parameterization. The deceleration parameter study finds an accelerating universe at late times. The transition redshift is found to be ztr = 0.89 ± 0.25. Also, we discussed the physical and geometrical properties of the model.