Jack lying to the citizens of Halloween Town?

He lies to them because he is trying to get them excited about the concept of Christmas which (as he makes clear at the end of the song) isn't something that even he really comprehends yet.

Jack decides that their understanding can take a backseat to at least being interested in Christmas. In order to facilitate this, he translates his stories into something they will 'get':

The original script makes it a little clearer:

Confident face evaporating, the Mayor skulks off.

Jack looks down at the faces tipped up toward him -- in the expressions, puzzlement replaces eagerness.

JACK: (to himself) Well, I may as well give them what they want.

Jack picks up his song again -- the showman once more:

As does the Penguin Active Reader book of the film:

Jack thought, "They'll never understand Christmas". Then he had a good idea. "Maybe they'll understand this" He looked at each of them very carefully and he spoke quietly and slowly. "There's a very old man in Christmastown", Jacks said. "He's big and round with long, white hair. His clothes are red and he flies through the night sky in a big red sleigh. He shouts loudly and laughs! They call him Santa Claus! He puts presents under Christmas trees inside every house.
When the children wake up in the morning, they find them. Then they open them."

There's a huge difference between lying, and saying something that turns out to not be true. For the former, you knowingly said something wrong. The latter includes situations where you told what you thought was the truth at the time.

Jack doesn't willingly lie to his fellow Halloween town citizens. Jack misunderstood some of the key features of Christmas.

In "What's This?", he is continually bemused by the idea of non-violent fun. Children throwing snowballs instead of throwing heads, absolutely no one's dead, ...
Jack doesn't understand a non-Halloween world. He can't process it because Halloween is so ingrained in his perception of the world.

He misheard "Santa Claus" as "Sandy Claws". He also misheard "sleigh" as "slay", and "reindeer" as "rain gear". So presumably, he overheard someone talking about Santa Claus, and mistakenly interpreted some homophones that have a "more Halloween" feel to them.

When he is introducing Christmas to the Halloween town citizens, he is talking about what he perceives Christmas to be. He's not lying, he just misunderstood, and is explaining it to people who have even less experience with Christmas than him.

I think the main confusion, or the idea that Jack is willfully lying comes from the break in the Christmas explanation, where he mumbles "Well, I may as well give them what they want."

It sounds like he is willfully deciding to give the people a fabricated explanation to get their approval, which is what (I think) leads you to think he intentionally lies.
But as I see it, Jack was simply mumbling to himself that "There's no point in explaining the feeling of Christmas; instead I'll talk about the frightening ruler of Christmas town."

He makes that decision because Halloween citizens, used to horrible things, will better understand a frightening overlord (Sandy Claws) than a feeling of warmth (Christmas).

As a general theme to the movie, Jack had a skewed perception even though his intentions were honest and benevolent.
The only thing you can really fault him for is that he had Santa taken, instead of celebrating Christmas concurrently with Santa. But again, this was not malevolent, merely misguided due to being excited. He probably even fooled himself with the "I'll give Santa a year off" idea he gets; instead of letting envy get the better of him.