Here is a solution based on atbegshi and answers packages.
The idea is to use answers that write contents of theorem, lemma to an external file (mtfile.tex), discard all pages (all contents of the main file https://tex.stackexchange.com/a/267555/71471) and then use the external file to output only theorems.
We use a newif test \onlytrue for only theorem and \onlyfalse for normal use.
Auxiliary environments used to save the original definitions of theorem and lemma.
\newtheorem{xtheorem}{Theorem}
\newtheorem{xlemma}{Lemma}
Complete code.
\documentclass{article}
\usepackage{lipsum}
\usepackage{atbegshi}
\newcommand{\handlethispage}{}
\AtBeginShipout{\handlethispage}
\newtheorem{xtheorem}{Theorem}
\newtheorem{xlemma}{Lemma}
\newif\ifonly % uncomment next line
%\onlytrue
\ifonly
\usepackage{answers}
\Newassociation{lemma}{mtlemma}{mtfile}
\Newassociation{theorem}{mttheorem}{mtfile}
\renewenvironment{mttheorem}{\begin{xtheorem}}{\end{xtheorem}}
\renewenvironment{mtlemma}{\begin{xlemma}}{\end{xlemma}}
\Opensolutionfile{mtfile}
\AtBeginDocument{%
\let\handlethispage\AtBeginShipoutDiscard}
\AtEndDocument{%
\clearpage\pagenumbering{arabic}
\let\handlethispage\relax
\Closesolutionfile{mtfile}
\Readsolutionfile{mtfile}}
\else
\newenvironment{theorem}{\begin{xtheorem}}{\end{xtheorem}}
\newenvironment{lemma}{\begin{xlemma}}{\end{xlemma}}
\fi
\begin{document}
\lipsum[1-12]
\begin{lemma}
this is some bla bla in lamma
\end{lemma}
\lipsum[1-12]
\begin{theorem}
some bla bla in lamma
\end{theorem}
\lipsum[1-12]
\begin{lemma}
some bla bla in lamma
\end{lemma}
\end{document}
