To have the enumeration start on a new line:
You can use \phantom{} to avoid the empty theorem text, while not providing an output.
Start the theorem environment, enter math mode and type \phantom, then press return. Then enter some text in the phantom box.
Move cursor to after the math mode box, and press Return for a new line. Choose enumerate layout in the dropdown, and press Tab to nest it in the theorem environment.
Having finsihed the enumeration, press Return twice to go back to the theorem environment, where you can the choose a different layout---e.g. proof.
In LyX, you get something like the following, with the phantomed not showing in the compiled.

Note: LyX has rich keyboard shortcut customization that we can use to insert the \phantom in a less fiddly manner: Go to Tools > Preferences > Editing > Shortcuts > New and in the Function field, insert math-insert \phantom{.} and assign it a shortcut.
Without new line:
Perhaps you are interested in an output identical to that of this MWE:
\documentclass{article}
\usepackage{amsthm}
\newtheorem{theorem}{Theorem}
\begin{document}
\begin{theorem}
\begin{enumerate}
\item Bla Bla Bla
\item Bla Bla Bla
\end{enumerate}
\end{theorem}
\end{document}
This compiles without the itemization starting on a new line:

To obtain this in LyX, you can label the theorem (Insert > Label) or insert an empty theorem title using an TeX code insert (Insert > TeX Code) with content []. The label option would look like this in LyX, and compiles as the above MWE:

theoremenvironment : interaction withenumerate/itemize– barbara beeton Feb 18 '20 at 18:27