Jarvan IV's quote "Today is a good day to die" is ultimately believed to come from the one of the Lakotan war chiefs, either Crazy Horse or Sitting Bull.
Jarvan IV's quote "Ours is but to do and die" is a reference to a line in The Charge of the Light Brigade by Alfred, Lord Tennyson.
Jarvan IV's quote "For my father, the king" is also spoken by Arthas from the Warcraft series.
In the Polish client, one of Jarvan IV's quotes is "We won't forsake the land we came from" (org. Nie rzucim ziemi, skąd nasz ród). This phrase comes form Polish poem Rota(The Oath), which was proposed to be Poland's national anthem after World War I.
Moved by Shyvana's plight, Jarvan IV assisted her in slaying the mighty dragon that killed her father. After the battle, Jarvan IV offered Shyvana a place as a noble warrior in the ranks of the Demacian Elite Guard. Out of gratitude and necessity, Shyvana accepted.
In Poppy's backstory, she delivers a helm that she and her father had made. This was said to have been very important, and also was described as having a jewel in the front, similar to Jarvan IV's helm in his classic skin.
After Jarvan IV was defeated and nearly executed by Swain and Urgot, people described him as "different". This lead to the speculation that for a period of time, LeBlanc replaced Jarvan IV.
However, according to speculations made based on a note, Jarvan IV was kidnapped and replaced by LeBlanc months after his Judgement was held. By looking at later issues of Journal of Justice, it is also possible to say that Jarvan IV was likely rescued by Katarina, thus he is no longer impersonated by LeBlanc.
Similarly, the fact that people described Jarvan as being "different" after his failure, and that his two year long journey is quite mysterious, are probably unrelated to this issue since both events occurred long before Jarvan IV even became a champion.
RiotRunaan stated that what was going on with Jarvan IV is very different from what the community thinks, so this theory is most likely false.
Jarvan IV once protested with Katarina about Heywan Relivash's involvement in the upbringing of Kalamandan War with Swain.