LaTeXUA

The table of content depth and numbering depth can be changed by adding in the preamble,

\setcounter{secnumdepth}{3}
\setcounter{tocdepth}{3}

Lyx does this automaticaly and can be set in "Documents > Settings > Numbering & TOC"

In the main.lyx file there is this option again commented in the user defined preamble

%%% ToC down to subsections
%\settocdepth{subsection}

%%% Numbering down to subsections as well
%\setsecnumdepth{subsection}

and again after \begin{document}

\setcounter{tocdepth}{2}

%subsections are added to the TOC
\setcounter{secnumdepth}{4}

%subsubsections are numbered

Normaly only the lyx option should be there, but for me it has not been working for the numbering so I uncommented the option in preamble %\setsecnumdepth{subsection}