I'll answer a couple bits of this from direct experience:

Rephrasing the question, can a person with no intent/desire lucid dream?
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Yes. Two people I have talked to about lucid dreaming had lucid dreams the very night after I told them about it. One of them was very upset by it and about the whole experience. It wasn't something he sought out or wanted or ever wants to experience again.

But what if someone with no intent/desire to lucid dream, does a lucid dreaming technique correctly, does that person have a lucid dream then? Or does nothing happen since they do not have desire to lucid dream?

I am wondering this because if all we need to do is get a technique correct, then we can lucid dream. Even without intention to do so.
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This seems a bit absurd, so I think maybe your question isn't worded exactly the way you intended. Why would a person who doesn't want to achieve lucid dream work on the disciplines or techniques involved in it at all? Just DOING it requires intent. I don't see how they can be separated. Are you implying that somebody could accidentally work on the techniques without understanding why?

Although... I recognized an aspect of FILD as possibly being part of my childhood experiences. I would very often go to sleep tapping my foot to some rhythm in my head. With some of the speculation about why FILD works, this could well explain my lucid experiences back then - and thus be an example of what you are trying to get at. So maybe your question isn't so absurd after all.

FWIW.