Dick Grayson of Earth-2 is the alternate version of Dick Grayson, the Robin/Nightwing from the main earth. Essentially he is the same character from the golden age who lives on Earth-2, but with several differences. In the silver age, he was introduced in Justice League of America #55 as a grown-up Robin, opposed to the teenager version from Earth-1. The concept has been recovered for the new Earth 2: Society series, this time becoming the third Batman of that universe, after the death of Thomas Wayne, the second Batman from Earth-2.
The life of Earth-2 Dick Grayson would be the same as Earth-1 Dick Grayson with subtle differences and happening at an earlier time: His origin is very much the same as Earth-1's Dick Grayson: his parents were killed in a circus accident and Bruce Wayne adopted him as his ward. Years passed, and so did time, with Batman and Robin soaring through Gotham City. However he never was part of any teenage team but in his adulthood he would join the Justice Society of America and in war time he was member of the All-Star Squadron. Also along with the Star Spangled Kid and with Power Girl they would form the Super Squad.
With time, Batman/Bruce Wayne decided to take a break from fighting crime and married Catwoman a.k.a. Selina Kyle. Grayson would choose to become a lawyer to pursue justice in the courts. In this work he would be successful enough to became part of his own firm (Cranston, Grayson & Wayne) and later would be elected as ambassador to South Africa.
After the death of Batman he returned to action as Robin, but joining up with Helena Wayne, daughter of his deceased mentor, with whom he would start a romantic relationship, but the two want to keep it distant so neither gets hurt. In the crime-fighting relationship, it was Robin who would be the one with mentor attitude and Huntress would act as the pupil.
As member of the Justice Society, the grown up Robin would meet both his own doppelganger from Earth-1 and with him he shared the feelings to having had to grow up in the shadow of Batman. Later he would had the chance to meet with Earth-1's Batman. But, as lawyer he had prosecute his own teammates, accused of treason as part of a plot by Per Degaton. Fortunately, the name of the JSA was cleared of any charges and Robin keep good relations with the team.
After the Crisis on Infinite Earth's, Earth-2 was destroyed with Grayson and Helena being destroyed by the Anti-Monitor's shadow demons. Their later appearances would be as flashbacks or hallucinations.
In 52, with the return of the multiverse a new Earth-2 appeared. This Earth-2 was home of the Justice Society Infinity and lacked of kryptonians. However this earth was partially explored, because of the Flashpoint reboot, but it was revealed than the romantic relation between Dick and Helena had become distant because the obsessive behavior of Huntress with hunt the Joker.
The original golden age version of Earth-2 Dick Grayson, along with Huntress would be seen again in Convergence, both still a couple and fighting against the Red Son Superman, before being returned to their timeline/universe.
New Earth 2 (post Flashpoint)
The life of Dick Grayson of the post Flashpoint Earth-2 was totally different. He never was Robin and instead he was married to police officer Barbara Gordon, both living in Chicago. Father of a child and working as reporter, the family Grayson survived in a world of wonders despite the attacks of Apokolips. But when Darkseid launched a final attack that devoured the planet and forced the population to escape in improvised spaceships, Dick had to fight to keep his family safe. However his wife died protecting his son. With the help of veteran boxer Ted Grant, Dick rescued his son and took him to a spaceship. Unfortunately, he would mix with the wonders of the earth in their battle to save the earth. After accept that earth was doomed Green lantern (Alan Scott) took Grayson along with Jay Garrick, Yolanda Montez, Thomas Wayne & Val-Zod to save them but all of them would be transported outside the multiverse.
The team would end in the world of Telos, an extra-dimensional planet created by Brainiac as receptacle of dead continuities. When they fought him Telos overpowered them. Despite that and from the erratic actions of Telos, the people of Earth-2 ran away for different paths. Along with Thomas Wayne, both heroes would start a pilgrimage where they would meet the pre-Flashpoint versions of the characters. Dick and Thomas later would end facing a lethal version of the Joker and several other Batman enemies. Surrounded but not willing to accept defeat, Thomas charged against the villains and detonated a bomb, killing himself but taking with him most of the villains. However Grayson and Joker survived. Hurt but alive, the Joker shot Dick, leaving him paralytic. However Dick was saved at last minute by Telos himself, who killed the Joker and cover Dick with a film of material that returned his mobility.
Trying to understand Telos, Dick accompanied him when Deimos attacked and revealed than Telos was human before, with a family. Feeling sympathy for Telos, Grayson insisted on convincing him to free the cities without a bloodbath. In the battle against Deimos, Dick would meet Superman (pre-Flashpoint version) who would inspire him to take the place of the fallen Thomas Wayne.
As consequence of Convergence, the entity Telos splits himself from the planet mass, and the planet itself became the new Earth-2, being returned to its own universe among the Earth-2 people. And with Dick Grayson taking the mantle of Batman.
One year later after planetfall, Dick Grayson uses the technology of Michael Holt to keep his back tied, because the technology from Telos failed after the entity vanished away. Grayson operates as the third Batman in the city of New Gotham, still searching for his lost son. His last case involves the hunt of Terry Sloane who has disappeared with a dangerous technology in his hands and scared of what is searching him. However when Sloane tried to activate the Source Vault he died from being struck by lightning, an accident caused by Val-Zod. Searching for Val-Zod, Dick clashed with the super-powered wonders. But he joined them when the last ship orbiting Earth-2, the Overwatch-One, start to falling towards the planet, helping them to avoid the catastrophe and joined them when they went against the mad Dr. Impossible.