The evidence is already clearly there. Even early on, their Combat/Reaction times are greater than their Travel Speed. Proof was already shown. Piccolo moonbusting. Took about 4sec for his attack to reach the moon and destroy it. It would take Light just under 4sec to go from the Earth to the Moon. That makes the attack shy of lightspeed. And that was when Piccolo was Weighted with a PL over 300. A stronger Piccolo was having his attacks evaded by Nappa. Make of that what you will. I've seen Luke feats and all of his major abilities require Time and Focus to perform. Something that he doesn't have here. And I can prove to you, that someone even Weaker than Goku in terms of destructive ability and speed, can take down Luke.
No, it would take light around 1.28416 seconds (the average distance between earth and the moon is 238,855 miles [LINK], divide that by the speed of light [186,282.4 miles/sec or 186,000 miles/sec] and that's what you get) to reach the moon, or about 1.3 seconds. Also, it wasn't given an official time-frame. If you're taking this from the anime, then it took around seven-to-eight seconds. In the manga, I have no idea.
Let's see here:
The beam fires at around 0:02-to-0:03 and the moon blows up at around 0:10, I am assuming that's when it hit.
238,855 miles / 7 sec = 34,122 miles/sec
238,855 miles / 8 sec = 29,856 miles/sec
It's still not light-speed, even if you use the anime. Relativistic, yes, but as I said before it has no official time frame (as far as I know) so that's still just a speculation. Also, ki blasts have inconsistent speeds. Sometimes they're fast, and other times Yamcha can dodge them. We would have to calculate the speed of those blasts you're talking about that Nappa evaded to accurately determine his speed.
That's just for the beam speeds, not for the character speeds which seem to be less impressive. Anyway, I'm not that good at math so take that all with a grain of salt.