At first, this concept seems off, like a way of getting around double jeopardy, but the more I think about it, the more it makes sense. Let’s consider the scenario in the OP, but a little different. Let’s imagine that the DA had instead decided not to charge the defendant with the additional charges related to arson, perhaps because the lying made gathering the evidence difficult, but still got the lying conviction. Now he’s at sentencing, except with no charges and conviction or acquital related to arson. Would he be justified in bringing up that he had lied related to their investigation on his potential involvement in arson or is it simply that he lied relevant?
I think, in general, most people would agree that the punishment for lying ought to depend on what they were lying about. Consider a woman who finds out that her husband lied to her about something. Maybe she asked him if he liked some new dish she cooked, he says yes, then finds out he gave most of it to the dog. Maybe she’s good and it was just one bad dish, or maybe she’s bad in general; she can’t be sure whether or not he likes her cooking in general, she’s only sure he lied about that one dish. Sure, she’ll be a little upset, but I don’t think it would devolve into a nasty argument unless they were already having problems.
Now imagine she asks him where he was last night and he says he was at Tony’s house helping him work on his car, but she had driven by there on some errands and his car wasn’t there. Maybe he was at the bar having some drinks and watching the game because he didn’t want to be home and watch some show she found boring and insisted on watching over the big game. Or maybe he was at Tina’s house sleeping with her. So maybe he just told a white lie to get out of watching American Idol instead of his Alma Mater’s big rivalry game, or maybe he’s cheating on her; based on that, she can’t be sure whether or not he’s cheating on her, she can only be sure he lied about that one thing. But I also think she’d be quite a bit more upset about it and it would probably lead to at least a big argument, or more if they were struggling. Yet, in both cases all she knows is that he lied.
So, it seems to me that context is always relevant when sentencing, otherwise why bother with a range on sentences and not just have a single punishment? So, in the case of the OP, the context of that lie is relevant, and the context is directly related to the other charges since that’s what they were asking him about when he lied. Regardless, they cannot exceed the maximum penalty for the crimes of which he was convicted, so if getting such a sentence seems to harsh, the problem isn’t so much with the judge and sentencing as it is with the law itself that allows such a harsh penalty.