There are those who cause sufferings. Some do it for the sake of pleasure. Others do it for a cause. One of those is Sahn-Uzal. A Warlord who carried a dark belief that that had him to terrorize settlements and tribes. This was in the hope of gaining a seat of the god's table, in the Hall of Bones. He was a man who embodied suffering.
On the other hand, there are those who can be saviors to the world. Some act as protectors. Others act as a shining hope to look at when the world you're in is filled with darkness. One of them is Veigar.
Veigar followed and practiced the mystical art that was found by an order of mages. With the celestial magic, it allowed him to give hope on Runeterra via the pattern of the star's movement. One followed the path to free others from their despair. Another followed the path of giving fear and agony.
After his death, Sahn-Uzal was filled with anger and torment when he realized the afterlife he was promised was false. Even with his belief shattered, he refused to fade. He refused to fade just like the other souls. Through deceit, he used dark mages to bring him back as a phantom. After killing them, he began his reign through his new name Mordekaiser. His reign brought massacre and destruction. During that path of destruction, he met a yordle that had the potential to support his reign of terror. Veigar
After getting captured, Veigar experienced torment and have done horrific actions in Mordekaiser's fortress. The magic that was meant to give others hope twisted for a darker purpose. After years of being locked up, what Veigar believed in shattered. Darkness and terror was the only thing he knew. After he escaped, instead of turning back what caused him pain, he decided to embrace the darkness and torment that was given to him.
While Veigar and Mordekaiser carry different motifs,
They still carry that same theme that has always been close to them. Torment and Fear. It is true other champions do fall under this theme as well. It is a theme that is general. Even then, their history together and the duality comes into play for both of them. This allows that theme to shine more between these two. Their beliefs/goals were opposed for one gave despair while the other one tried to stop it. Both were in a situation of torment. Despite it, they embraced it. Mordekaiser mostly controls the afterlife. It became this way for death showed him his belief was a lie. Veigar became an evil warlock because of Mordekaiser. The one who gave him dreadful agony. Because of that, he modeled himself just like his captor, wanting to cause fear and suffering to others. Since they follow a similar path and goals, the likelihood of meeting with one another is inevitable.
This is all I have for now. I could keep on discussion more but I feel as if I will be stretching my idea a bit much. Even then, I hope you enjoyed this post even if it is a long one. Hopefully, you gained something from this. :P