No you are rested as if it were a normal dream. But it's not easy to keep focused on something while lucid dreaming, you will likely forget that you are in a dream and no longer be lucid.
But reading text coherently in a dream is, AFAIU, quite uncommon as you suggest. I used to lucid dream regularly and deliberately as an adolescent. I would hesitate to say you can't focus in a lucid dream--consciously focusing on elements of the dream, or trying to shape the dream, is kind of the point of lucid dreaming. (Of course, what you have most control over is yourself.) But, yeah, you can't usually control things in such fine detail for the duration necessary to coherently manipulate it. Reading any non-trivial text in a dream isn't very common, lucid or not-lucid, AFAIU. Though, I would imagine it's more common for people with experience lucid dreaming.
I'm sure some people can read and write as much as they want, but at a certain point on the curve we're probably dealing with people with abnormal neurology. Sort of like how there's memory palaces and other mnemonic techniques, which anybody can learn, and then there's people with Hyperthymesia.
I've had enough lucid dreams when I was kid to know the difference. These days lucid dreaming for me is rare and not deliberate--i.e. if I have the presence of mind to wake up in a dream, it's mostly by chance, not because I orchestrated it through habituation. It came mostly naturally as a kid, after I stumbled upon a reproducible technique. Adults usually have to practice at it, and I'm just too lazy (and too tired). The vast majority of my dreams now are non-lucid, or quasi-lucid (i.e. I'm not in deep sleep) such that I know it's not like a proper lucid dream. The experiences are quite different.
Given the sibling comments, this is clearly not a fact. It's best to avoid stating opinion/experience as fact.