In this work, we have performed first-principle calculations to investigate the electronic properties, structural stability, and lithium migration pathway of 2D Ti ₂CY ₂/Graphene (Y = O, S) van der Waals (vdW) Heterostructure. The heterostructure formed by O and S functionalized MXene and graphene layers are separated by 3.04 and 3.40 Å exhibiting weak vdW interaction. It is found that the intercalation of lithium (Li) atoms in between the Ti ₂CY ₂/Graphene layers is thermodynamically more favorable in comparison with intercalation on the top or below the heterostructures. The Bader charge transfer analysis confirms that O atoms gain less charge -0.13 e during Li intercalation compared to S atoms with charge transfer of -0.47 e due to the larger size of the 3p orbital of S atoms. Each Li atom contributes ~0.88-0.89 e during the intercalation process. As O is more negatively charged in comparison with S atoms in the heterostructures, Li atoms are more localized on the Ti ₂CO ₂ layers with a tendency to form chemical bonds with Ti ₂CO ₂ layers while they are less localized on the Ti ₂CS ₂ layers creating lesser chemical bonds. The diffusion energy barrier is lower for Ti ₂CS ₂/graphene than Ti ₂CO ₂/graphene during Li intercalation. The NEB study also confirms that the activation energy barrier decreases with the increase of intercalated Li atoms for both the heterostructures indicating that Li atoms exhibit weak repulsive interaction causing weak Li binding with the heterostructures as they increase in number. Both the Ti ₂CO ₂/graphene and Ti ₂CS ₂/graphene heterostructures can be considered promising anode materials for Li-ion batteries due to their structural stability, and lower diffusion energy barrier.