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In an article, I need the counter for Theorems (Lemmas), like Theorem X.Y. But, somewhere I do not need the counter for the Theorems, for example: in preface/appendix or somewhere else like Theorem.

Q: How to define the environment for the Theorem or Lemma.

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With amsthm you can define a new theorem environment using

\newtheorem{theorem}{Theorem}

If you want an unnumbered version similar to this, then use

\newtheorem*{theorem*}{Theorem}

Use the theorem* environment inside the preface or appendix, and theorem elsewhere. Here is a minimal example:

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\documentclass{article}

\usepackage{amsthm}

\newtheorem*{theorem*}{Theorem}
\newtheorem{theorem}{Theorem}

\begin{document}

\begin{theorem}
This is a numbered theorem.
\end{theorem}

\begin{theorem*}
This is an unnumbered theorem.
\end{theorem*}

\end{document}
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