Start new page with each section

The titlesec package allows to do this with just

\newcommand{\sectionbreak}{\clearpage}

It's cleaner than what you were doing and the package also allows to completely customize sections. Here's a fully compilable code sample showing how it works:

\documentclass{article}

\usepackage{titlesec}
\newcommand{\sectionbreak}{\clearpage}

\begin{document}

Text

\section{Title}
Text
\subsection{Title}
Text
\subsection{Title}
Text

\section{Title}
Text

\end{document}

Obligatory ConTeXt solution:

\setuphead[section][page=yes] % or page=right

The accepted answer in that form won't work as expected in LyX. This solution causes problems when the document includes a ToC and hyperref support: It makes the paging of the hyperref links be off-sync with the document paging (e.g. clicking on Section 3 which is on p4 will take you to p3 instead).

As mentioned in the comments, this happens because by default LyX is loading hyperref before titlesec. To work around this you can use \newcommand{\sectionbreak}{\clearpage\phantomsection}.

Alternatively, in LyX, you can include in Document Settings > Local Layout:

Provides hyperref

And then load hyperref manually in the LaTeX preamble, like this:

\usepackage{titlesec}
\newcommand{\sectionbreak}{\clearpage}
\usepackage{hyperref}