That seems really unlikely, and it's certainly never been done before.
On the one hand, Lightray is pretty stupidly powerful. The guy's created a star, show molecule manipulation abilities, some pretty heavy energy absorption across all spectrums, including life force energy from Orion, etc. And yeah, he seems like he reacts at the speed of light and he can travel at even faster speeds.
On the other, his actual combat record against bricks is pretty uninspiring. Outside of a single owning of Mongul (admittedly, an LOL moment) in a series of dubious continuity, he's had problems with more physical foes like Kalibak and Orion (losing to both, multiple times). I think Ikaris might fall into that arena.
Beyond that, I don't think Ikaris' little tricks are going to work. He's not a great telepath, and with the New Gods' even spotty resistance (sometimes they're totally immune, sometimes not, sometimes motherbox and will power help, etc) I don't htink it's going to be a factor. Certainly Lightray is a better energy projector. But Ikaris, as an Eternal, is crazy durable, and he's an extremely fierce warrior, so I give him a solid win over Lightray.
Meanwhile, I think Orion/Thor is incredibly close, maybe a 50/50.
Team 2. I don't think Ikaris is going to be able to catch LR. He's such a puss that he would likely just fly around going all fast and stuff and fight at a distance.
That's what Lightray SHOULD do, but whenever he fights a physically dominant foe like Orion or Kalibak he tends to come in closer than he should. He's twice been defeated by Kalibak this way, where he might have won if he had stayed away, and once by Orion when he was insane and evil. He tackled Takion when he was evil/insane as well, rather than trying to fight from a distance.
It's his thing, he's not a great tactician, he's a great strategist.
Orion and Kalibak are some of the best fighters in comics. And they both have sticken it to Superman. I don't think Ikaris has that kind of credit. So LR would still beat him IMO. When Ikaris can take it to Thor or Gladiator, then he would be on Orion or Kalibak's level. But he can't. So Ray would still win IMO.