I'm new to Lyx, so these might not be elegant solutions. Another Lyx
user helped me last week, so here is my attempt to pass on the favor.
--------------
To put a double space between chapter headings and section headings in the ToC:
Put in the preamble:
\usepackage{tocloft}
Put underneath your chapter titles (in the body of your text) in ERT (Ctrl-L):
\addtocontents{toc}{\vspace{0.35cm}\endgraf}
---------------
To change to single spacing in a section, put this in ERT (Ctrl-L)
before the section:
\begin{spacing}{1}
and then this in ERT after the section:
\end{spacing}
----------------
I don't know if this is the text you mean, but to change the chapter
heading text size, you will have to put something like this in the
preamble:
\chapterfont{\centering\normalfont\large\bfseries}
I hope this is helpful.