Is this worth reading if I dropped the main story...? This looks like a better story.........

I only read this one and I understood it well. They do appear in the other story and show their 2nd child so maybe its worth skimming?

It's the first story the author released for this universe, but it's not the main story. It's even part of another series. The stories just take place around the same time and there are connections between the stories and some characters. But you can read it without reading KML.

What is the main story?wanna try to read it

Kiss me liar
Warning the art kinda ugly

There is no real main story I think. "Kiss me liar" is the first story the author released for this universe, probably one of the reason was that the MC is a korean, at least I think that was a factor.
And earlier this year she said "Desire me if you can" was the first she came up with, but released it 10 years later -this year... .

The author made clear very early that she was writing two series for this universe "...if you can" for the Miller family consisting of 6 stories and "Kiss me...." also consisting of 6 stories. Even the titles were known years ago. And she also worte a few titles not being part of those series.
If you go by release "Kiss me liar" was the first, and after that "Kiss me if you can".
If you go chronologically. "Kiss me liar", "Kiss me if you can", and "Run away if you can" take place around the same time, but "Eat me up if you can" and "Lick me up if you" can would come before. For the Miller you actually have 3 generations.

For manhwa's only "Kiss me liar" and "Kiss me if you can" were adapted.
If you want to read Kiss me liar, be warned, most really don't like the dynamics, it's toxic.
Keith is a pretty notorious trash ML and Yeonwoo lacks backbone most of the time when it comes to Keith.

I like this one way better than kiss me liar