Prompt for inserting label when using theorem style environments in latex

Question

When inserting the environment equation (by C-c C-e equation) in latex-mode, emacs shows a prompt to insert a label. It is desirable to have the same prompt for a theorem-style environment like lem defined in the document. When I do C-c C-e lem, the environment lem is correctly inserted, but a prompt for setting the label does not appear.

What is the procedure in order to have this prompt?

\documentclass{article}
\usepackage{amsmath,amsthm}

\newtheorem{thm}{Theorem}
\newtheorem{lem}[thm]{Lemma}
\begin{document}
\begin{lem}

\end{lem}

\begin{equation}
  \label{eq:1}

\end{equation}
\end{document}

Answer 1

If you have an up-to-date version of AUCTeX, say from ELPA, you have 2 choices:

1.) Set something like to this in your init file:

(with-eval-after-load "latex"
  (add-hook 'LaTeX-mode-hook
    (lambda () (add-to-list 'LaTeX-label-alist '("lem" . "lem:"))))
  (when (boundp 'reftex-label-alist)
    (add-to-list 'reftex-label-alist
                 '("lem" ?m "lem:" "~ref{%s}" nil ("Lemma" "lemma") nil))))

2.) Set the information on a per-file basis in the local variables of your .tex file:

%%% Local Variables:
%%% mode: latex
%%% TeX-master: t
%%% eval: (add-to-list 'LaTeX-label-alist '("lem" . "lem:"))
%%% eval: (add-to-list 'reftex-label-alist '("lem" ?m "lem:" "~ref{%s}" nil ("Lemma" "lemma") nil))
%%% End:

You need the second eval only when you're using RefTeX.

Then open your .tex file, hit C-c C-n so that AUCTeX parses your lem environment and you should be set.