Installing a fresh version of lua-mode on Emacs 29.1 I got several warnings such as:

In lua-find-regexp:
lua-mode.el:994:2: Warning: docstring has wrong usage of unescaped single
    quotes (use \= or different quoting)

It seems that the byte compiler started warning about some quoting mistakes in docstrings starting with Emacs 29, and single-quotes now need to be escaped with \=. Apparently the unescaped single-quotes can be rendered incorrectly.

I escaped the single-quotes, except for some which were paired. I changed those to backquote/single-quote pairs like `foo'; it seems that these pairs are fine.

The only byte-compiler warnings I saw after were for three docstrings wider than 80 characters, and I left those alone.