Ground rules: The term Green Lantern can be applied to any one of the policing power ring slingers across the Galaxy. In this fight the Green Lantern in question is the most well known GL of Earth, Hal Jordan.
Goku is the most powerful Sayian in the Dragon Ball Z universe. Like fine wine, he only gets more powerful with age and training, so although he may outclass GL today, I’m using the Goku from when I was familiar with the show: the Goku from the Cell Saga. The arena is a canyon surrounded by a mountain range and wide-open desert. These guys need their space.

Personal bias: Dragon Ball Z was a fun show. I always liked the energy-based heroes/villains and DBZ had no shortage of them. Speaking of energy, GLs power ring is far and away my favorite concept for a superhero. I can’t say Hal Jordan is my favorite character, but if I could be any hero, it would be a Green Lantern.

Fight! Green Lantern powers up his ring and takes to the sky. He doesn’t gain much altitude, just enough to see over walls of the canyon. He lands once he secures high ground. No sign of Goku. Hal forms a pair of high-powered binoculars with his ring and scans the horizon behind some cover. Then he spots a man leaping into the air. Hal traces the arch through the sky onto one of the highest visible peaks. Target acquired…with a canyon’s length between them.

The ring gives Hal an estimate of his opponent’s power level. It is enough to make him want to get the most out of the element of surprise. Also acting fast seems appropriate as the power level seems to be increasing with time. He fires a beam from his ring into the canyon. It weaves in and out of the crevasses deep within until the ray of green light is ready to emerge from the other side. By the time the beam is directly under Goku’s mountain, it detonates into a green fireball. Goku falls into the canyon.

Goku catches a stone cliff and pulls himself under a cavernous overhang. He sees the sky glow emerald as his opponent scans for a body. Goku’s chi is now fully charged. He makes the transition to SuperSayian. With a burst of power that sends a shockwave through the valley, he rockets into air.

Hal and Goku’s flight path intersect with an impact that shifts every grain of sand in the valley. Green Lantern spirals out while Goku’s stays the course straight upward. Hal tries to make a visual, but it appears his opponent went directly into the sun. The blinding light gets impossibly brighter as Hal is engulfed in white-hot energy and pummels the Earth.

Hal is hurt, but the adrenaline takes over. His ring notifies him of Goku’s recent spike in power levels, information GL didn’t need. The ground around him ignites with a flurry of energy blasts. Hal imagines a shield and it forms overhead. It holds, but Hal knows that it could fall to a focused blast. He also knows the best defense is a good offense.

Green Lantern takes flight along with four other constructs of himself to draw away fire. He builds a small fleet of fighter jets with his mind that materialize behind his opponent. Before Goku can react, he is surrounded in Sidewinder missiles.

Green Lantern prepares to continue the assault when he hears something from inside the cloud of dust and green smoke: “Kamehamaha.” Hal swiftly returns the oncoming attack with a storm of raw energy of his own. The two blasts connect, each trying to overcome the other. For this instance, there is no Hal Jordan or Goku, only dueling wills and the power they command. It is a brief moment that ends in a draw. The feedback launching each fighter miles in opposite directions. The dessert is now a valley of super-heated glass.
Goku is the first to recover and decides to take the combat in close. Hal thinks his eyes deceive him when Goku appears instantly before him. He knows it is real with the first point of impact. A jab to his side. A knee to his stomach. A roundhouse kick to his head. Hal’s only defense against Goku’s lightning fast martial arts is his ring’s automatic shield, but it is not nearly enough. His mind is too weak after holding back the kamehameha. With a last thought Green Lantern sends out a distress call to the Justice League and the Guardians of Oa, but it is too late.

Results: Goku wins. Although GL matched him in power, Goku’s Superman-like strength and super reflexes were too much to counter.