As Seamus commented, most classes already start chapters on a new page. This requires using the \chapter command.
However, if you use \section commands, page breaks would not automatically happen, this is not very common for smaller sections. But you can define it, by this modification in your LyX document preamble:
\let\stdsection\section
\renewcommand*{\section}{\clearpage\stdsection}
The first line stores the original \section command with a different name, then \section is redefined to include a \clearpage before. A good effect is, that \clearpage forces figures and tables to be printed out before the next page is started, so they don't float into the next section. That's why I did not use just \newpage.
However, I strongly recommend using a class with \chapter commands, such as book, report, memoir, scrbook or scrreprt. The last two are from the great KOMA-Script bundle.
Indentation on the first paragraph can be forced in this way.
Insert into Document->Settings->LaTeX Preamble this line:
\usepackage{indentfirst}
However that appears in lyx
Best Answer
You can try going to Document --> Settings --> LaTeX Preamble, and add
(Normally one would need
\makeatletterbefore and\makeatotherafter, see What do \makeatletter and \makeatother do?, but LyX adds this automatically, so it is not necessary.)