In this manuscript, we have considered the Finsler-Modified Randers Cosmological Model (FMRCM) with cosmological constant \(\Lambda\) for generalized Finsler-Randers space-time, to investigate the solutions of this model in Lyra theory with Bianchi type- \(IV_0\) model of universe of cosmology under different variations of energy conditions such as the null, weak, dominant and strong energy condition with cosmological constant. Further, we have analyzed the role of cosmological constant \(\Lambda\) in various framework, exploring its impact on both the accelerating and decelerating phases of cosmic expansion. Additionally, we have showed that for \(\Lambda = 3K\) where \(K>0\) is any real number, the null, weak, and dominant energy conditions with cosmological constant are satisfied while the strong energy condition with cosmological constant is violated. This violation is interpreted as the cause of the accelerated expansion of the universe, but for \(\Lambda = -3K\) , all energy conditions are satisfied, indicating no evidence of cosmic acceleration. These results are supported through both graphical and geometrical analysis.
