Your problem might be hidden in some settings that are not shown at the moment... Hence, the complete generated LaTeX code would be helpful. At least I found some information that was not mentioned before:
that you are probably using the package booktabs because of \toprule etc. Hence, you seem to have created the table by inserting TeX code/ERT into your child document.
what exact document class your main document and your child document have -- I assume "presentation (beamer)" for both.
Here I give a MWE that works for me as expected. The output is

The LyX file looks like

and here is the generated LaTeX code (very few lines are removed).
%% LyX 2.0.5.1 created this file. For more info, see http://www.lyx.org/.
\documentclass[english]{beamer}
\usepackage[T1]{fontenc}
\usepackage[latin9]{inputenc}
\makeatletter
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Textclass specific LaTeX commands.
% this default might be overridden by plain title style
\newcommand\makebeamertitle{\frame{\maketitle}}%
\AtBeginDocument{
\let\origtableofcontents=\tableofcontents
\def\tableofcontents{\@ifnextchar[{\origtableofcontents}{\gobbletableofcontents}}
\def\gobbletableofcontents#1{\origtableofcontents}
}
\long\def\lyxframe#1{\@lyxframe#1\@lyxframestop}%
\def\@lyxframe{\@ifnextchar<{\@@lyxframe}{\@@lyxframe<*>}}%
\def\@@lyxframe<#1>{\@ifnextchar[{\@@@lyxframe<#1>}{\@@@lyxframe<#1>[]}}
\def\@@@lyxframe<#1>[{\@ifnextchar<{\@@@@@lyxframe<#1>[}{\@@@@lyxframe<#1>[<*>][}}
\def\@@@@@lyxframe<#1>[#2]{\@ifnextchar[{\@@@@lyxframe<#1>[#2]}{\@@@@lyxframe<#1>[#2][]}}
\long\def\@@@@lyxframe<#1>[#2][#3]#4\@lyxframestop#5\lyxframeend{%
\frame<#1>[#2][#3]{\frametitle{#4}#5}}
\def\lyxframeend{} % In case there is a superfluous frame end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% User specified LaTeX commands.
\usepackage{booktabs}
\makeatother
\usepackage{babel}
\begin{document}
\lyxframeend{}\lyxframe{test slide}
\begin{table}
\caption{Caption of table}
\label{tab1}\centering\begin{tabular}{@{}l cccccc @{}}
\toprule
&\multicolumn{2}{c}{M1} &\multicolumn{2}{c@{}}{M2} &\multicolumn{2}{c@{}}{M3}\\
\cmidrule(lr){2-3} \cmidrule(lr){4-5} \cmidrule(l){6-7} &C &SE &C &SE &C &SE\\
\midrule
Variable 1 & 12.345 & * & 23.456 & *** & 34.567 & *\\
\midrule[\heavyrulewidth]
\multicolumn{7}{@{}l}{* $p < 0.05$, ** $p < 0.01$, *** $p < 0.001$.}\\
\end{tabular}
\end{table}
\lyxframeend{}
\end{document}
lyx, is there maybe more setup information you should give out to enable others to replicate the problem you're experiencing? (I don't uselyxat all, so I'm afraid I can't help you.) – Mico Mar 17 at 23:45