What LanternCorps would they be in? [Eomer]
Green Lantern Corps, as Éomer does possess a lot of willpower. During the battle of Helm's Deep, he fought side by side with Aragorn and together they killed a lot of orcs, until they were overwhelmed and forced to split up (Aragorn and Legolas remained on top of the ramparts, Éomer and Gimli were forced to retreat into the Glittering Caves).
Aragorn is a Dúnadan, so his stamina and will to keep on fighting for a long time is to be expected. Éomer has a connection to Númenor and a trace of Gondorian blood through his grandmother, but that's about it. He's basically just a regular guy, who can go toe to toe with Aragorn due to his sheer willpower. And yes, the Rohirrim are special in a way that they can see far better in the dark than most men and they are taller and broader than most Gondorians, but compared to Aragorn, Éomer's lineage is far more ordinary and he has none of the magic talent and longevity.
And sometimes Green Lanterns also have to think outside the box, as (to make the story exciting) their constructs are rendered ineffective by something at first until they find a way around it. And Éomer showed ingenuity when he lead the attack against the hundred of orcs who had (unbeknownst to Éomer) Merry and Pippin in their clutches, with only fifteen men of his own, and he ended up losing only two of them. He and his Éored ended up winning by using guerilla tactics and psychological warfare, by picking the orcs off at night and stalling them with an ever tightening ring of attacks, until daylight either finishes them off or forces them to retreat. The orcs were stuck inside a secured parameter and they had two choices: try to break through and get stabbed by a Rider's spear, or stay put and burn to a crisp. To make them panic and lure them into making bad decisions, Éomer tightened the ring more and more (allowing Pippin and Merry to crawl away from the orc that kept them, while the orc was still stuck).
And all this shows that Éomer is capable of prolonged direct combat but also of a more creative type of combat if the situation demands it. / @therapardalis