\documentclass[a4paper, 12pt]{article}

\begin{document}
\section{LilyPond snippets in a footnote}

Test for snippets in a footnote\footnote{Here's the footnote:
\lilypond[fragment]{c' e' g'} }:
\marginpar{ Yes, even as marginpar
\lilypond[fragment]{c' d' e'} }

\end{document}