Certain medical treatments involve the introduction of exogenous liquids in the lungs. These liquids can form plugs within the airways. The plugs propagate throughout the branching network in the lungs being forced by airflow. They leave a deposited film on the airway walls and split at bifurcations. Understanding the resulting distribution of liquid throughout the lungs is important for the effective administration of the prescribed treatments. In this paper, we investigate numerically the splitting of a liquid plug by a two-dimensional pulmonary bifurcation under the influence of a transverse gravitational field. The splitting is characterized by the splitting ratio, which is the ratio of volume of the liquid plug in the daughter channels and depends on the capillary number and the orientation of the bifurcation plane with respect to a three-dimensional gravitational field. It is observed that gravity induces asymmetry in the splitting, causing the splitting ratio to he reduced. This effect is mitigated as the capillary number is increased. It is also observed that there exists a critical capillary number where the plug will not split and will instead propagate entirely into the gravitationally favoured daughter channel We also compute the wall stresses on the bifurcation walls and observe the locations where stresses and their gradients are the highest in magnitude.