lie - one meaning is to put yourself in a resting position lay- is the past tense of the above and it also means to put SOMETHING or SOMEONE else in a horizontal resting position or place it somewhere. So when reading the wonderful very hungry caterpillar 🐛 it means the egg was resting on the leaf

As far as I understand it "To lie" refers to one's self. "To lay" refers to putting something down. So I lie down in bed and lay the book next to me. But this gets tricky because the past tense of "to lie" is "to lay" so many people get them mixed up, you can see in the attached picture. I will say that a lot of native speakers use them interchangeably, so in casual conversation you could use either most people wouldn't notice. Funny experience I have with this word and why I know this: my mom makes fun of me for saying "I'm going to lie down" because it sounds weird, despite it being correct. She says "I'm going to lay down" as a lot of people do, even though that is not correct. So the message is, unless you're writing an advanced English essay, don't worry about the difference too much. :)

The verb ‘to lie’ has two past tenses, for different meanings of the word. He lies all the time. (Says something false, present/timeless). He lied yesterday. (Said something untrue in the past) He lies on the bed once a day. (Puts himself on the bed, present/timeless). He lay on the bed yesterday. (He put himself on the bed in the past.) The book is a classic written for small children and is written with the simplest English tense, the past. As far as whether it’s natural, natives often confuse lay/lie and to my ear the past tense of lie, second meaning, sounds a little awkward, and would surely sound even more awkward if I hadn’t heard and read this very book thousands of times. Colloquially we very well might say ‘was lying’ to avoid that awkwardness. But using that here would destroy the beauty of the work!