As
@Tosk points out,
that was Unkar Plutt. And really for me this is the single most compelling piece of evidence that Rey's parents were nobodies that neglected and abandoned her. I mean the guy is obviously a scum bag. Not the kind of person a caring parent would trust with their child's well being.
There's more to Jakku than just Niima Outpost and for all we know that ship is just a sublight junker they use to haul scrap from one side of the planet to another. Or it does have a hyperdrive, but for them, Jakku is just a frequent stop off point to trade and refuel, so that they at some point came back and died there isn't beyond the bounds of possibility. Indeed, they managed to get in enough debt once to necessitate selling their offspring (the implication being the ship was more valuable to them than Rey was) so it's likely they screwed up again at some point and it lost them their ship and/or their lives.
It's not impossible, but really I think the question was answered quite sufficiently in TFA and this little bit in TLJ is just to reemphasise for those that missed it the first time. That aside, I think it's a much more compelling narrative is that Kylo was being entirely honest the whole time. For all his faults, this is a guy that believes himself to be in the right and I think genuinely wants to persuade Rey to see things as he sees them. Lying to her would be pointless when the truth is so much more convincing.
As for his account of Luke's "attempted murder": again, he wasn't lying because that's what he saw from his point of view. He awoke suddenly to the sight of his uncle standing over his bed, weapon drawn and murder in his eyes. The whole thing was over in a second, but it was enough for Ben to feel mortally threatened and reflexively defend himself. After that, there really wasn't an opportunity for the two of them to exchange notes.
If there was any lie there on Kylo's part it would be one of omission. Specifically that he'd already decided to turn on Luke at that point (which is almost certainly what drew Luke into his room that night to begin with.) But again, from Kylo's perspective that's not a relevant piece of information since Luke's actions only reaffirmed his decision.