A example of it:" my failure lay in that I was too lazy to do any exercise."

I personally think it's not correct. But some people think the other wise.

Thank you.
Grammatically and structurally, I suppose it is correct; all the preposition requires is a noun object, which condition the noun clause fulfils.

I was tempted for a moment to suggest that a prudent the fact would not be amiss (my failure lay in the fact that I was too lazy to do any exercise)-- but then I was minded of the cries of 'redundancy!' that would arise. The problem, I think, is just the awkwardness of it, not any error. Let's change it to my failure was that I was too lazy to do any exercise.
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Thank you very much , Mister Micawber. I am the one who asked the question. And that REALLY was my first time saying anything here. You gave me a lot of encouragement.

I want to go on with the discussion. Since it is definitely not correct to say " Despite that it was raining outside, he ran out." I suppose it's equally wrong to use a "that clause" after "lie in". Or maybe that's just the way people say it?

Thank you again.
Yes, further searching for an example convinces me that I cannot make a decent object of a preposition from a that-clause without inserting the fact or some other noun to make an appositive out of the clause. How odd. They work as subjects and verb objects well enough.

Your lie in + thatclause seemed uniquely, I say in retrospect-- possible to me for some other reason: maybe it was just my stylistic antipathy to the fact. So it is not the way that people say it (or should say it); it's just how I perceived it in your question.
What is ergative in English?, can you make some examples of this so that i can understand it.
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There is no ergative case in English, but there are ergative verbs. There's a good description and examples at [url=" "]WIKIPEDIA[/url]. The example I use with my students is the wind blew my hair / my hair blew in the wind.