When considering the relationships among big cats, lions and tigers are more closely related to each other than either is to cougars. Both lions (Panthera leo) and tigers (Panthera tigris) belong to the same genus, Panthera, and share a more recent common ancestor. This genetic closeness is evident in their behaviors, physical features, and broader social structures.
On the other hand, cougars (Puma concolor), while they are also large felines, belong to a different genus, Puma. This genetic distinction highlights a further evolutionary divergence from the lineage that led to lions and tigers. Hence, the most closely related pair among the given options is lions and tigers.