That sounds like a nice way to do it, too. I heard about it before, but don't know R, so I didn't really consider it.
The reason I chose lmt is that it correctly keeps the markdown language syntax of the code blocks. That means I can put my literate config into my Zettelkasten [1] or [2] and watch it pretty-print in the browser.
There are also literate [3] and org-babel [4], but I don't think they are future proof. .lit is a random format and .org basically requires Emacs+orgmode.
For lmt/markdown: I believe yes, to the extend the editor allows for it. It is seemingly just like regular mardkown code blocks. I get the correct syntax high-light in the ``` code blocks. I don't have lint/LSP setup yet (currently moving to Neovim), so I can't say anything about that.
Literate/.lit: I don't know, I guess not.
Emacs/orgmode: Yes, this also does syntax highlight. And you can edit the code-block in a separate window as if it was a "real" source code file. I've been using this for almost two years now. Personal opinion: I don't think the benefits of Emacs outweight the cons.
I just played around with R the other day and it would use MD too to generate HTML/PDF.
It uses Knitr.
https://kbroman.org/knitr_knutshell/pages/Rmarkdown.html