Finding a legal way to read 'The Lady Wants to Rest' online is straightforward. It's officially available on the serialized fiction platform KakaoPage in its original Korean. I found it there myself. They have a decent official translation available, and you can read quite a few chapters for free to see if you like the vibe. The translation quality is consistent, which matters a lot with these kinds of stories.
If you're not into Kakao's interface, I've also seen it pop up on Manta and Tappytoon. They're both legitimate apps that license content, so you're supporting the creators. Manta has a flat-rate subscription model, which is great if you binge a lot of comics and novels. Tappytoon is more pay-per-chapter, but they often have events. Honestly, sticking with these official sources is the move—the updates are reliable, and you avoid the weird, ad-ridden aggregator sites with machine translations that butcher the characters' personalities.
A quick warning: some fan translation sites might list it, but they tend to disappear or drop projects randomly. It's frustrating to get invested and then have the source vanish. Paying a bit for the official version is worth it for the stability and to ensure the author gets something for their work. The story's chill, slice-of-life vibe is best enjoyed without the chaos of sketchy sites.