In LyX it is easy to make a theorem with multiple parts. It involves using the enumerate environment nested in a Theorem environment. But the resulting parts are numbered (1), (2), et c. To get alphabetically numbered parts, use the following LaTeX inserted code.
\begin{itemize}
\item[(a)] < PART ONE >
\item[(b)] < PART TWO >
\end{itemize}
Roman numerals can be used also, by replacing the “a”, “b” and so on.