Marked partially_translated because I'm missing the double entendre.

I know Tewi lies a lot, but I dont get the double meaning, fast explanation?

...I don't get the double meaning either. That's why I marked it as partially translated. And also left a comment explaining that that was why I had marked it as partially translated.

maybe because she could be lying about not lying next year? then again with japanese love of puns I doubt it...

Perhaps it also means "I plan to stop being untrue (Unfaithful)"

That's the only thing I can come up with though

That's not it. I think it has to do with the multiple readings of "yameru", one of which is "to retire", implying Tewi's old age (she is over 1200 years, after all).

However, I think the oni are just laughing because that seems like a really obvious lie, even for Tewi.

All that aside, Tewi is unbearably moe in that first panel.

It's Japanese saying that "Oni (ogre) laughs when you tell about next year's things." It means "It's too early and worthless."

Anyway, Tewi is so cute :)

I'm virtually sure it's not yameru, and it can't be the oni thing because it's not a double meaning. That leaves Kstead's explanation as the most plausible, although it's not very convincing. :\

That's definitely not it, though. That "unfaithful" meaning is not present in "usotsuku" (be a liar).

Tewi says that she's gonna stop lying starting next year, but since next year didn't start yet, everything she says now can possibly be another lie. Sly girl.

it is just another lie, next year she will stop lying. then how about now? she still lying, so what she said is a lie too. That means she won't stop lying next year.

To me I interpret it as a classic logic loop. It would have been the same if she said "I always lie" to me.

Further explained, if she says she'll stop lying next year, then since it is still the time before she said she'd stop lying, she could still be lying about stopping her habit once next year rolls around. Basically what she says now, that she'll stop lying next year, can't be trusted because she could still just be lying.

Good ol logic.

Maybe post #431607 is related?

Nope, that's a pixiv April Fools meme.

According to http://www.languagerealm.com/japanese/japaneseproverbs_ra.php , there is an applicable Japanese proverb, just as dan564 said:
"来年のことをいうと鬼が笑う"
"When one speaks of things of next year, oni laugh."
English equivalent:
"Prediction is difficult, especially about the future."

Basically, to make predictions or promises for the coming year is pointless. Promises are just words; determination, and the actions that it brings about, are what counts.