If the deer population increases, they would consume more grass, which is their food source. This increased consumption would likely lead to a decrease in the plant (grass) population. Consequently, if the plant population diminishes, it might affect the deer population in the long run, as they may run out of food.
As for the lion population, if the deer population were to increase initially, the lions might have more food available, potentially leading to an increase in their population as well. However, over time, if the grass population decreases significantly, the deer population would likely decline, which would ultimately affect the lions.
Given these considerations, the most immediate and directly correlated outcome of an increase in the deer population is:
The plant population would decrease.