Here’s the magic code for your document settings -> LaTeX preamble to get run-in headings:
% makes 4-th level (SubSubSection) headings run-in
% page 154 of memoir manual
\setbeforesubsubsecskip{0ex}
\setsubsubsecindent{\parindent}
\setaftersubsubsecskip{-1ex}
What is a run-in heading? Normal headings are on their own line. Run-in headings have the text immediately following on the same line.
This is a heading
This is the body text that is in the paragraph. This is the body text that is in the paragraph. This is the body text that is in the paragraph. This is the body text that is in the paragraph. This is the body text that is in the paragraph. This is the body text that is in the paragraph.
This is a run-in heading. This is the body text that is in the paragraph. This is the body text that is in the paragraph. This is the body text that is in the paragraph. This is the body text that is in the paragraph. This is the body text that is in the paragraph. This is the body text that is in the paragraph.
Now, if anyone knows how to make this appear in LyX by editing the layout file, I’d love to hear it.