Numbering of Lemmas in Appendix

I’m preparing a paper using the Lipics style and have a long appendix: each appendix Section is headed by capital letters A,B,C… I would like to have the numbering of Lemmas in the appendix such as Lemma A.1 (if it is in appendix A), resp. Lemma B.1, B.2,… (in appendix B) etc. Any hint? I tried to redefine the thetheorem variable and played with it for a while, but was not succesful, I’m not very strong at LaTeX.

Thanks for possible hint! Here is a minimal working code:

documentclass[a4paper, USenglish, numberwithinsect]{lipics}
theoremstyle{plain}
newtheorem{proposition}[theorem]{Proposition}
newtheorem{observation}[theorem]{Observation}
newtheorem{conjecture}[theorem]{Conjecture}
newtheorem{problem}[theorem]{Problem}

title{Title}
author[1]{Peter Franek}
affil[1]{Affil}

begin{document}
maketitle

begin{abstract}
abstract
end{abstract}

section{Introduction}
label{s:intro}
begin{theorem}
Theorem 1
end{theorem}
begin{lemma}
First Lemma
end{lemma}

appendix
section{first appendix chapter}
Some text..
begin{lemma}
I don't want Lemma 1.1 but either Lemma A.1 or Lemma A.1.1
end{lemma}

end{document}